Using complex variables, evaluate the following integrals: xp- x +1 1.0 sinx -d.x x(x² + a²)* 2. , where " is real.

Q: cos(8) cos (sin(0)) de

A:

Q: Use the substitution u = x + Vx +5 to evaluate the definite integral dx I = Va2 +5 Give an exact…

A:

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: I = ∫dxx2x2-64   Put,          x = 8 secθ        dx = 8 secθtanθdθAlso,          θ = sec-1x8

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x²e-9r³ dx +C

A: ∫x3e-x3dx

Q: | (44 + 313 dx = Evaluate the integral using an appropriate substitution. NOTE: Enter the exact…

A: Let I = ∫ x3dx/(4x4+3)3 ---(1)

Q: Evaluate the integrals using fundamental theorem. Write answer as exact value not approximation. a)…

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9e" + 8e-X dx…

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. 9e dx 1+e2=…

A:

Q: Evaluate the integral. -1 6 sinx dx = 2 +C NOTE: Enter the exact answer in expanded form.

A: Given that: ∫6sin-1xdx

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Given I=∫x3x2+81dx       Put x=9 tan θ            dx=9 sec2θ dθ      I =∫9 tanθ3 9 sec2θ…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x²e dx +C

A: The solution of the problem is given in the next step.

Q: Evaluate the integral using the formula x dx = E. (Give your answer as a whole or exact number.) /…

A:

Q: 5 ( (x2 + 1)z dxp x8

A: I = ∫(x2+1)52x8.dxI = ?

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: Given information:

Q: Evaluate the integral. (Use C for the constant of integration.) sin3(0) cos“(0) de

A: Here,

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sec?…

A:

Q: Use the rules for definite integration and Jc dx= c(b - a) to evaluate the integral Į 3 dx. 3 dx =|…

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 2(1 + tan?(a)) da 2…

A: We will solve this problem in following steps

Q: (a) Use the substitution rule to show that sin(√) dx = [ 2x sin(x) dx. (b) Use integration by parts…

A: To show: (a) The result ∫sinxdx=∫2xsinxdx by using the substitution rule. To find: (b) The value of…

Q: In Exercises , use a substitution to change the integral into one you can find in the table. Then…

A: 27. Given integral is, ∫x3+x+1x2+12dx.   It is integrated as follows:

Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos(6) cos (sin(6)) de

A: The power rule of integration states that ∫vndx=vn+1n+1.

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos?x sin 2x dx

A: This question is based on Indefinite Integral.

Q: C for the constant of integration.) Evaluate the definite integral. (Use sin(23x) xp 1 + cos (23x)…

A: The given integral is,

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: Given:

Q: sin-cos-sino de has the form - 2 The resulting integral of + C. What should be the value of 0 to…

A: To evaluate the integral ,use the following trigonometric formulas.

Q: 5. Use trigonometric substitutions to evaluate the integral: I Væ(4 – #)dx.

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. S sec² x 81 -…

A: The given integral is: I=∫sec2x81-tan2xdx    ...1   As we know the common integral.…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. (4x – 3)º dx…

A:

Q: r H+ sin x sin 2x dx 2 cos X

A: Solving the problem by finding the value of the integration.

Q: Use the Table of Integrals to evaluate the integral. 6 1 dx X 4x 7 Select the correct answer. The…

A:

Q: valuate the integral using the Trigonometric Substitution metho x² (81-x²)3/²2 dx

A: Topic:- application of integration

Q: x tan? V1 – x2 sec? V1 – x2 V1– x2

A: Consider the integral: I=∫x tan2 1-x2 sec2 1-x21-x2dx……1

Q: (1-x+2x²-x³ -dx x(x²+1)²

A: NOTE: Refresh your page if you can't see any equations. . first, we need to use the partial…

Q: Use u-substitution to evaluate the following indefinite integrals. Giv your final answer in terms of…

A: see 2nd step

Q: Evaluate the indefinite integrals using Substitution. (use C for the constant of integration.) dz…

A: In this question, we need to evaluate the integrals using substitution method.

Q: Using the trigonometric substitution, the integral dx (x2 - 16) Vx2 – 16 I = is equal to the…

A:

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral…

A:

Q: sec x+ cos x COS.X dx 2 cosx

A: Given query is to evaluate the integral.

Q: Evaluate the integral. 3 sin-x dx +C %3D

A:

Q: evaluate using trigonometric substitution. Refer to the table of trigonometric integrals as…

A: Given Data The integral is ꭍx²dx/(1- x²)3/2.   Let,

Q: x2 dx Vx? – 4x + 5

A:

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer.…

A:

Q: 5. Which integral requires more work to evaluate? sin“ x cos“ x dx 798 sın x cos x dx or Explain…

A:

Q: Using appropriate substitution and taking a + 0, 3tan(ax) the integral S dx is equal to: cos² (ax)

A:

Q: x³ dx 3. S V(x2-9)3 (x²–9)3

A:

Q: Evaluate the integral. T/6 | 9 sec'x dx 2. п/6 |9 sec?x dx = 3/3 (Type an exact answer.)

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. J tan6(9x)…

A: The objective of the question is evaluate the indefinite integral with substitution method.

Q: Evaluate the integral. NOTE: Enter the exact answer. 1 + 11/x| dx 13x3 J+C

A:

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x3 (3x²+2)³ J…

A: Given: I=∫x33x4+23dx     ...1   As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1