1 8.) / dx (x2 + 16)3/2

Q: Evaluate the following integrals.

A:

Q: Evaluate the following Integrals. dx V1 – 4.x2 4. -

A:

Q: Find the exact value of the following improper integral: ex L x2 dx

A:

Q: Evaluate the following integrals dx V9 - x?

A: Given that, ∫x29 - x2 dx           ...(1) We can do this with trigonometric substitution. Consider,…

Q: dx 8. J3 x-3)3/2

A:

Q: 6.) | dx 4 – x²

A: Let the given integral is ∫x34-x2dx

Q: 4) Evaluate the definite integral: S, (2x² – 4x + 6)dx. -

A:

Q: Evaluate the following indefinite integrals S xe3x² dx and S (x + 4)lnx dx.

A:

Q: Evaluate the following integrals using dx = -00 (a) 7xe- dx (b) 13 xe-X dx

A:

Q: Evaluate the following integrals: dx

A:

Q: Find the value of the following integrals using the method of residues. 00 .2 x + 3x + 4 Lo (x² +…

A: To find - Find the value of the following integrals using the method of residues.

Q: Sx² tan x3 dx (In x)3 dx 4x 2x3 dx x++1

A:

Q: 12.) / 5a2 – 14x + 6 dx 23 – 3r2

A:

Q: 1. Evaluate the following integrals, Debe Justify all steps. x + 4 dx x3 + 3x2 – 10

A: Given:-             fx = x+4x3+3x2-10To determine                     ∫ fx dx

Q: 5х — 2 dx x² +1 - 10.)

A:

Q: 2х 3 2. Ver + 2 dx

A:

Q: Q1) Evaluate the following integral using By Parts Method: х.In(x3 + x) dx

A:

Q: 4. S)(1-x²)dx 5. S(e2t)dt

A:

Q: In x dx 7.) /

A:

Q: 5. Evaluate the following improper integrals (if not shoW Wny). x² dx a- 00 4 1 dx -2 x+2 b-

A: To evaluate the improper integrals.

Q: T6 Based on the image attached, differentiate each of the following integrals with respect to x.

A:

Q: ~2 .4 x* +1 dx 1 J1

A:

Q: Use any appropriate method to evaluate the following integral: (x^3)*(e^(x^2)) dx

A: Simple Integration problem....

Q: 1. Evaluate the following integrals using integration by parts. x5e* dx

A:

Q: A. Evaluate the following integrals using the different methods of integration dx 1. (9 + x²)3/2

A:

Q: 2. Evaluate each of the following integrals using the indicated technique (additional techniques may…

A:

Q: 2. 21-/9 – 4ª dx

A: The by parts method is given as ∫uv=u∫v-∫u'(v) where u is the first function and v is the second…

Q: Evaluate the following indefinite integrals. 1. S(5x + 4)11 dx 2. Sx (x² + 2)17 dx 3. fx²(9 – x³)5…

A: The solution is given below

Q: Evaluate the following improper integrals or show that they diverge. c+00 dx (a) x5/2 1 dx 1+ x2 (b)

A: Let's find.

Q: 2. x² V1-x? dx_

A:

Q: Evaluate the following indefinite integrals: S (5.x2 – 3x)(2x + 4)dx а.

A:

Q: Evaluate the following integrals: x +1 1- dx (x² + 2x + 2)3

A:

Q: Evaluate the following integrals. 1) La7 dx Ans. 4 1 v1-2x-x2

A:

Q: Evaluate the following integrals. Reasonable work is expected! 1.) 4x²e" dx

A:

Q: 3. Find each of the following integrals using any suitable techniques : 12.r3 – 2x2 + 6x – 3 dx - -…

A:

Q: Q1) Evaluate the following integral using By Parts Method: y = х.In(x3 + x) dx

A:

Q: 2+(ln x)3 5. J x(In x)2+In x) ах

A:

Q: dx 2.) S 4+ x2

A:

Q: y V3 x dx 8y-y2

A:

Q: For which of the following integrals should substitution be used, instead of Integration by Parts?…

A: Solution :option D substituition be…

Q: Evaluate the following integrals ii. fx cot-'x dx .

A: Solution is given below:

Q: Evaluate the following indefinite integrals. 1. Jx²dx 2. S(x³ + 2x)dx 3. S(a)dt :a = constant

A: Solving the problem by finding the indefinite integral.

Q: Evaluate the following integrals: 2r3 2) 2x2 + 1 - dx x² - x 1) | dx

A:

Q: S, 3x²e* dx .2

A:

Q: Evaluate the following integrals.

A: ∫x91-x20dx=∫x91-x102dx Now put, x10=t⇒10x9=dtdx⇒x9 dx=dt10

Q: / FVA 12.) dx x²/25 – a²

A: Given integral is ∫1x225-x2dx Substitute x=5costdx=-5sintdt

Q: 2. dx

A: Given: ∫ x3ex4-3dx

Q: Evaluate the following indefinite integrals. 1. [(5x + 4)¹¹ dx 2. √x (x² + 2)¹7 dx

A:

Q: 4. S2-*(5 – x)³dx

A: To integrate the given function