Evaluate the indefinite integral by using the substitution u =x° +x to reduce the integral to standard form. S+)* (sx* + 2x) dx dx =

Q: Evaluate the integral. 3 x e* dx = +C

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Q: dx I = a² +x²

A: Given query is to find integration of the expression.

Q: 1. S(In x)² dx

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Q: he resulting integral of dx is ax + b ln x -Arctan +C, where a, b, d, e, and x3-2x2+5x are integers.…

A: b=2

Q: 14e" dx 1+ e20

A:

Q: Consider the indefinite integral dx: (26 – 8)° - This can be transformed into a basic integral by…

A: A detailed solution is given below.

Q: Evaluate by algebra dx 1. S 3 1+ √x+1

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Q: evaluate the given integral. L (ex + e-x)/2 dx

A: To evaluate, ∫ex+e-x2 dx

Q: Q2) Find the integral of: f*,6 tan*x dx

A:

Q: Find the indefinite integral. 2+ 4x + 3. dx B+ 6x² + 9x + 2 Step 1 du/dx dx Let u = Begin by…

A: The given integral,       ∫x2+4x+3x3+6x2+9x+2dx

Q: Find the indefinite integrals: (a) S dx x+1 + C. (b) S da = 23 x2+1 =

A: SOLUTION-

Q: Find the indefinite integrals, if possible, using the formulas and techniques.

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Q: Evaluate the integral. -^x dx e S² sin √1-x² 2

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Q: Find the following indefinite integral. +2e -0.1x dx

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Q: Find the following indefinite integrals. (» /= +1 dx. (a) x2 (b) / : re dx. xe' 2.x +1 dx. x2 +1 (c)

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Q: Find the following indefinite integrals. dx Vx + 2 +C !!

A: To evaluate the integral: I=∫xx+2dx...(1)

Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx =…

Q: dx 51. 1 + e*

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Q: dx I = е. a² +x²

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Q: Find the indefinite integrals: x5/2 + 4x + 1 dx a) / ? b) / (a" 6t7 2 + Te' ) dt t3

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Q: Q2) Find the integral of: 6 tan*x dx

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Q: dx a proper or improper integral? Why? (x-3)? .3 Is So 1

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Q: Find the indefinite integral.

A: ∫ exex+12dxSubstitute u =ex+1=∫ u2duApply the Power Rule:  ∫xadx=xa+1a+1,    a≠-1=u2+12+1Substitute…

Q: Find the indicated integral (if it exists) / e bx dx e12z +1

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Q: The indefinite integral Vx +1 dx may be solved by substituting u = x² +1 to get | vūdu. O True O…

A: ∫x2+1dxPut x2+1=udifferentiate w.r.t.x2xdx=dudx=du2xdx=du2u-1I=∫udu2u-1 Therefore it is false that…

Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: Evaluate the following improper integral. Give an exact answer. 1. dx 2/3

A: Given that ∫051x23dx, we have to evaluate the following improper integral.

Q: Find the integrals below. a) |e2x dx b) S 3 dx

A: We have to find integrals of a)∫e2xdx b)∫3xdx

Q: 2. Find the following indefinite integrals. 1 (a) dx J x/16 – [In(x)]?

A: We have to solve

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: cos (78) dx, u=7

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Q: dx. х2 + 4 3.

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Q: Find the following indefinite integrals 1. Sx(x² – 2)5 dx

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Q: Find the following indefinite integrals. dx = (m) / (~- (bị + 3e" + dt =

A: (a) I1 =∫x3-1xdx (b) I2=∫eπ+3e2t+1etdt We know that  ∫xndx=xn+1n+1+c and ∫enxdx=enxn+c

Q: dx I = S %3D a²+x2 e.

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Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

Q: Evaluate the definite integral integral a=0 and b=1    7/ 1+x2 dx

A: Refer to the question, we have to solve the definite  integral a=0 and b=1    7/ 1+x2 dx.

Q: Find the indefinite integral

A: To evaluate: ∫2x+1ex2+xdx Let substitute t=x2+x dtdx=2x+1dt=2x+1dx Substituting the value,…

Q: 5. Jxе2x dx

A:

Q: a) Evaluate the integrals using appropriate substitutions. dx Sine i) S ii) S de Cos? 0+1 1+16x?

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate the integral: x² e3a dx

A: This question is related to Indefinite Integral, we will use Integration by parts formula to solve…

Q: 8. dx Evaluate the improper integral if it exists O.

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Q: (d) L™ x³ cos(x* + 5) dx. (e) f(2x – 1)³ dx . -

A: For the given integral  ∫0π4x3cos(x4+π2) dx

Q: Find the integral of e*cos (x)dx

A: The given integral is:∫excosxdx.We will use integration by parts formula to evaluate the above…

Q: Evaluate the integral. 5 x2 e dx +C

A:

Q: Find the integral of (1 + 2x)e^(-x) dx from x-0 to x--. A. 3 B. 4 C. 2 D. 1 O A B. DI

A: Use integration by parts for solving it,

Q: 6. Sxe -3* dx хе

A: We solve the above integral using integral by parts which is given in step 2 .

Q: 3. Find the integral: L,x*dx

A:

Q: Evaluate the integral. 2 e 1/x5 dx

A: Rewrite the function as follows: ∫12ex-5x6dx