*In 3 et + e* dx -2r In 2 e – 2 + e

In 3 et + e dx -2r In 2 e – 2 + e

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 1E

See similar textbooks

Related questions

Q: Improper integrals Evaluate the following integrals or state that they diverge.

Q: Evaluating integrals Evaluate the following integral.

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

Q: DEFINITE INTEGRALS Evaluate each of the following definite integrals: 21. ²(6x² + 3)dx 22. (4x+1)dx

A: To evaluate the integral.

Q: Evaluating integrals Evaluate the following integral.

Q: Evaluating integrals Evaluate the following integral as they are written.

A: Given:

Q: Integrals Evaluate the following integrals.

Q: Integrals Evaluate each integral.

Q: Improper integrals Evaluate the following integrals or state that they diverge.

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: To Determine: evaluate the following integral .include absolute values only when needed. Given: we…

Q: .3 onsider the indefinite integral a - Va + 9 dr: This can be transformed into a basic integral by…

A: Given query is to transform the integral in u and du format.

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: We have to evaluate ∫e5+xxdx Using substitution method, let t=5+x Differentiating with respect to x,…

Q: Evaluating integrals Evaluate the following integral as they are written.

A: We first integrate with respect to y.…

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Given: ∫0ln3eyey-123dy for evaluating given integral we substitute ey-1=t…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Given: I=∫e2xe2x+12dx for evaluating given integral, we substitute e2x+1=t…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Consider the following integral: ∫0555xdx Substitute 5x=u→5dx=du→dx=15du in the above integral:…

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Given: ∫-∞-21z2sinπzdz

Q: Improper integrals Evaluate the following integrals or stat that they diverge.

A: Solution - Given function - f(x)=∫7∞dxx+113 Let,t=x+1Differentiating w.r.t 'x',dtdx=1dt=dx…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: ∫e2x4+e2xdx Put, 4+e2x=t⇒0+2e2x=dtdx⇒2e2x dx=dt⇒e2x dx=dt2

Q: Improper integrals Evaluate the following integrals or stat that they diverge.

A: The given function is f(x)=1x2We have to evaluate the integral ∫3∞dxx2

Q: A. Indefinite Integrals + C. Evaluate the following integrals. dx x + x3 1 Ans. In x² 1 + x²

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: To evaluate I=∫ex+e-xex-e-xdx

Q: Directions: Evaluate the following definite integral. 1. L,(x- 3x2 + 1)dx 2. L,(x3 – 4x)dx

A: Question 1,Given, ∫-22x4-3x2+1dx

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: To evaluate I=∫72xdx

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Here given integration as I=∫12e3ln xxdx consider ln x=t⇒1xdx=dtAlso x→1, t→0x→2e, t→ln 2e

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Consider the following integral: I=∫-∞aexdx=∫-∞aex12dx=∫-∞aex2dx Substitute x2=t→12dx=dt→dx=2dt in…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Integration: ∫0π24sinx. cosx dxLet us take a substitution sin x=zcos x dx=dzx0π2z01

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Given: ∫1e2ln x5xdx Use substitution to solve Let ln x =t1xdx=dtwhen x=1,…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: We have given ∫x2 6x3+8 dx Take x3+8=t⇒3x2dx=dt⇒x2dx=dt3 Then, ∫x2 6x3+8…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Given, The integral ∫0π2sinx1+cosxdx.

Q: Improper integrals Evaluate the following integrals or stat that they diverge.

A: To evaluate the integral given below and to determine whether the integral is solvable or…

Q: Improper integrals Evaluate the following integrals or stat that they diverge.

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Consider the following integral: I=∫dx2-x3 Substitute 2-x=t→-dx=dt→dx=-dt in I:…

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: ∫1∞dxx-13 Now, limt→∞∫1tdxx-13=limt→∞∫1tx-1-13…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

Q: Improper integrals Evaluate the following integrals or show that the integral diverges.

A: Given- ∫-∞∞x31+x8dx To evaluate- The above improper integral. Concept Used- The above integral can…

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: Consider the provided improper integral, ∫-22 dp4-p2 Evaluate the following integrals. Apply the…

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: We have to solve the integral I=∫3-2x dx

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

Q: Evaluating integrals Evaluate the following integral.

A: ∫01∫0x2ex2 dy dx On integrating, we get ∫01∫0x2ex2 dy dx=∫012ex2·y0x dx=∫012ex2·x-0 dx=∫012xex2 dx

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: It is given that I=∫-1110x dx The given integration can be written as I=∫-11ex ln10dxI=∫-11ex ln10dx…

Q: Improper integrals Evaluate the following integrals or state that they diverge.

A: The given integral is ∫08dxx3

Q: Improper integrals Evaluate the following integrals or state that they diverge.

Q: Integrals Evaluate the following integrals.

Q: Integrals Evaluate the following integrals. Include absolute values only when needed.

A: Given integral is ∫x24x3+7dx

Question

Integrals Evaluate the following integrals. Include absolute values only when needed.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

To evaluate:

$\int_{\ln 2}^{\ln 3} \frac{e^{x} + e^{- x}}{e^{2 x} - 2 + e^{- 2 x}} d x$

Step 2

We have,

${(e^{x} - e^{- x})}^{2} = e^{2 x} - 2 + e^{- 2 x}$

Thus,

$\int_{\ln 2}^{\ln 3} \frac{e^{x} + e^{- x}}{e^{2 x} - 2 + e^{- 2 x}} d x = \int_{\ln 2}^{\ln 3} \frac{e^{x} + e^{- x}}{{(e^{x} - e^{- x})}^{2}} d x$ . . . (1)

Substitute, $e^{x} - e^{- x} = u$ $\Rightarrow (e^{x} + e^{- x}) d x = d u$

Therefore, (1) becomes

$\begin{array}{rcl} \int_{\ln 2}^{\ln 3} \frac{e^{x} + e^{- x}}{e^{2 x} - 2 + e^{- 2 x}} d x & = & \int_{\frac{3}{2}}^{\frac{8}{3}} \frac{1}{{(u)}^{2}} d u \\ = & \int_{\frac{3}{2}}^{\frac{8}{3}} u^{- 2} d u \\ = & {[\frac{u^{- 1}}{- 1}]}_{\frac{3}{2}}^{\frac{8}{3}} . . . Using \int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C \\ = & {[\frac{- 1}{u}]}_{\frac{3}{2}}^{\frac{8}{3}} \\ = & - \frac{3}{8} + \frac{2}{3} \\ = & \frac{- 9 + 16}{24} \\ = & \frac{7}{24} \end{array}$

Step by step

Solved in 3 steps

Knowledge Booster

$Indefinite Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN: