b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S x²+2x+1 x-2

Q: x3 1+x² dx

A: Note : according to our guidelines I can solve only one question, please reroute the remaining one.

Q: 2 (In x)² x3 da

A: Introduction: The definite integral of any function can be expressed either as the limit of a sum…

Q: sinhx dx 1+ coshx ) A 1+ coshx B (1+coshx)? (1+coshx)² D 1+ coshx

A: We have to find

Q: 7/4 2 sec(6x)dx sin(r In(x)) 13x 1

A: (b)

Q: (3x + 1)'3 dx

A:

Q: 1. . x + 4 dx x² + 5x – 6

A:

Q: sinh In(2+2x) dx? x+1

A:

Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

A:

Q: 2. S (4x³ + 2x²) cos(2x) dx

A:

Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: Find √√3 x² +3 x² +1 dx

A:

Q: 3x2[x18 + x15 sinh(ax³)] dx

A: Given that ∫3x2x18+x15sinh(ax3)dx, 3∫3x2x15sinh(ax3)+x18dx Take u=x3→dudx=3x2,…

Q: x2+1 - dx x4-x²+1

A:

Q: 4 fcos 3x sin³ 3x dx

A:

Q: 1 dx J 2/3 (1+ x/3)

A:

Q: (In x)² dx 3r

A:

Q: x4 x² x² + 1 - 1 dx ii) Š 1+ Inx

A: Please refer to the image below

Q: 4. x(x² – 1)² dx

A: Solution:

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: ) dx+ 2(y+×yナ>)dy

A: we have differential equation of is not exit...

Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: x²dx 3 2 3 (5-x') 2.

A:

Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

A:

Q: 1. S Vx4 – 10x3 + 25x² dx -

A: Solution: As per our guideline we are supposed to answer only first question . Kindly repost other…

Q: 1. (4xy? – 6y³)dx + (x³ – 8x?y + 9xy²)dy : |

A: Substitute x=yv

Q: 2 dx I (x + 1)(x² + 1)

A:

Q: Compute 1 2te-82 dx. x4

A:

Q: 2.x +1 dx. J 6x +x-15 (ii)

A: