y = (x – 1) 2x – x² + arcsin(x – 1) %3D - - - O - 12x – x² O - 2/2x – x² O V2x – x2 O 2v2x – x²

Q: Find the integral

A: Integrate∫3xx−2dx

Q: Calculate the integ ral In (2X +1) dx 2x +1

A: Here we have to calculate I=∫ln22x+1(2x+1)dx

Q: L ܛ 2 [T+ ] 3 + 16% ܓ

A: Given integral:- L=∫0131+16x212dx

Q: Express in exact form: In(x² + 1)dx

A: The definite integral is given as .The aim is to express this form in exact form.Concept used :Apply…

Q: y=x3 2

A:

Q: x- 3 +C 4 dx3D - 17+6x – x² +3arcsin = - V7+6x – x²

A: Show that ∫x7+6x-x2dx=-7+6x-x2+3arcsinx-34+C

Q: Integrate from 0 to 2

A:

Q: Is the answer correct?

A:

Q: dx X +T 2. 3.

A: Given ∫x32x3+πdx

Q: y = arccos /1 – x (1-x) 2 1 (1-x) 2 2 JA (1–x) 2 1 (1–x) 2

A:

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: 5x*dx V1 – x³ .5

A:

Q: 3/41 x² 3/5 √2x³-1 dx.

A: Consider

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A: Consider the integrals, ∫-11xx2+13dx…

Q: 1 dx x2 + 9

A:

Q: Find the integral (4x2 – 21x) dx (x – 3) (2x + 3)

A: The partial fraction decomposition or partial fraction expansion of a rational fraction is an…

Q: Let z = 6exv , find dz %3D

A:

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 1. Show that | (4x - 6x + 1)dx = (4x3 - 6x + 1)dx + (4x3 – 6x + 1)dx

A: Given ∫154x3-6x+1dx=∫134x3-6x+1dx+∫354x3-6x+1dx

Q: Find the integral -3x2 + 9x + 21 dx (x + 2)²(2æ + 1) ||

A:

Q: Evaluate: 2 (1) (2-3)* dx 1 1 dx x + 5 (2)

A:

Q: 5x 2 Evaluate: f fx fdz dy dx 2

A: