Evaluate the integral. 3x cos 2x dx O e3x [2 sin 2x - 3 cos 2x] + C 13 O 1 [2 e3x sin 2x + 3 cos 2x] + C 13 O e3x [ sin 2x + cos 2x] + C O e3x [2 sin 2x + 3 cos 2x] + C 13

Q: 3 19 dx Evaluate 5+x - 4x 2

A: By using complete square and integration

Q: 2.r³ – 5x²+4x– Ar 4 dx

A: Given:  ∫2x3-5x2+4x-4x2-xdx           =∫2x-3+x-4x(x-1)dx            =∫2x-3 dx+∫x-4x(x-1)dx By using…

Q: 7x² dx Vx² – 16 - +C

A:

Q: 3x – 11 dr (x – 5)(x – 3) Evaluate + C

A:

Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: Show that In (x+ Vx? + 1) x2 x + Vx2 + 1 dx x + / 2v x² + 1 X + V x2 + v2 +1 + 1 Vx+ 1 x2 + 1

A: This is a derivative problem

Q: Compute the following. 6 8x4- 30x³+33x²–11x +19 dx

A:

Q: dx 4x2 + 9

A: Use substitution.

Q: Find the integral 52? + 3х — 2 dx +C x3 + 2x?

A:

Q: Evaluate fcot (x) cos²x dx

A: The given integral: ∫cotxcos2x dx.We need to evaluate the above integral.