Find the integral [(3x² – x) In(3x)dx .

Q: Evaluate the integral.

A:

Q: evaluate the integral.

A:

Q: dx 2 x² +3

A: The derivative of x2 + 3 is 2x a part of it, which is x, is present in the numerator of the…

Q: Evaluate the integral. '2 (x - 8|x|) dx -1

A:

Q: Evaluate the integral ∫dx/ x√x4 - 1

A: We have given the integral;

Q: Find the integral ∫dx / √1−2x−x2.

A:

Q: ** dx x+3 x-1

A: Given: I=∫x+3x-1dx For evaluating given integral, first we simplify given expression then integrate…

Q: b) Evaluate the integral In 5 (x + 1)²e* dx

A: Given integral is ∫0ln5x+12exdx

Q: EVALUATE THE INTEGRAL: dy x 1+2x3410

A:

Q: The improper integral dx x²+4x+8

A: We solve this integration with the help of some basic formula of integration and sone basic…

Q: Find the integral ∫ dx / x3+1.

A:

Q: 2 dx x3 - x

A: We will find the integral as following.

Q: Find the integral dx √=x² + 6x I

A: We know that ∫dxa2-x2 = sin-1xa+C

Q: Evaluate the integral. -1x dx fcor-lx de 13) COS

A: Please rate and feel free to ask any query about any part of the question.

Q: dx 1. S 1-x2

A: Given:           ∫dx1-x2       =-∫1x2-1dx      =-∫1(x-1)(x+1)dx  Perform partial fraction…

Q: Evaluate the integral f e² In (x²+1)dx

A: ∫e2ln(x2+1)dx

Q: Find the integral. хебх dx (6x + 1)2

A:

Q: Find the integral ∫dx / √(x2+1)3.

A: Let x = tanu Hence, √(x2+1)3 = sec3u dx = sec2u du

Q: Evaluate the integral 6 dx (x+1) (x2+4)

A: Given,

Q: Evaluate the integral. V3 x3(x?) dx 1

A:

Q: e*dx e2x +1

A: We know that; ∫axdx=axlna+C And ddxcot-1x=-11+x2   Given: I=∫7cot-1exexdxe2x+1   ....1

Q: Evaluate the integral. x³ - 6 dx +ク 11 X

A:

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

A: Given,

Q: Find the integral. -3 4Vx dx X.

A: Given,        ∫-3x3-4xdx

Q: Find the integral of dx V1 – x²

A: Solve by integration

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

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

Q: sih (x) dx 6+x2

A:

Q: Find the integral ∫dx / (2x−1)(x+3).

A: We use partial decomposition

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) -

A:

Q: X- S2 *dx

A:

Q: Evaluate the integrals ∫dx/ {x(x + 1)(x + 2)...(x + m)}

A:

Q: Find the integral ∫ dx / x2−5x+7.

A:

Q: The improper integral| dx x²+4x+8

A:

Q: Find the integral ∫πdx / √π−x2.

A:

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

A: The given integral is:∫-2x+4x2+1x-1dxWe need to evaluate the above integral.

Q: In 2X dx Find the integral of J!

A: Find the integral using substitution method

Q: Find the integral of f(x³ + 1) Inx dx

A: Given :∫x3+1lnx dx

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: Evaluate the integral. 1 X - 4 dx x2 – 5x + 6

A:

Q: -dx e2a

A: Given: ∫01xe2xdx

Q: Evaluate the integral. x* dx x* – 1

A:

Q: Find the integral +C 1 dx x² – 16

A:

Q: Consider the integral 3 x2 dx 81- r /2

A:

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: 1 dx 1+ 3x x2

A:

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

A:

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: Find the integral. J (x³ + 4x– 3) dx -

A:

Q: Find the integral. J (x³ + 4x– 3) dx

A:

Q: Evaluate the integral J 1 dx 9+x2

A: Given,             ∫19+x2dx