Question

I need help integrating by parts the below

Integral of x^2 (e^(4x) + 3)

Answer 1

In google paste:

online math integration calculator

When you see list of results click on

Integral Calculator • With Steps

When page be open in rectangle Calculate the Integral of … paste:

x^2 (e^(4x) + 3)

and click Go!

When you see results click on:

Show steps

Answer 2

Lots of writing here, I suggest you look up the Tabular method

----- diff. -- integ
+ | ... x^2 .. e^4x + 3
- | ... 2x ... (1/4)e^(4x) + 3x
+ | ... 2 .... (1/16)e^(4x) + (3/2)x^2
- | ... 0 ... (1/64)e^(4x) + (1/2)x^3

∫( x^2 (e^(4x) + 3) )dx
= (x^2)((1/4)e^(4x) + 3x) - 2x((1/16)e^(4x) + (3/2)x^2) + 2((1/64)e^(4x) + (1/2)x^3)
= (1/4)e^(4x)(x^2) + 3x^3 - (1/8)x e^4x - 3x^3 + (1/32)e^(4x) + x^3
= (1/32)e^(4x) )(8x^2 - 4x + 1) + x^3

Here is a great video that explains this shortcut

https://www.youtube.com/watch?v=2I-_SV8cwsw&t=695s