What is the integral of x3 ex4 dx?

Answer 1

∫x3ex4 dx = 1/4ex4 + c

To solve, let y = x4, then:

dy = 4x3 dx

⇒ 1/4dy = x3 dx

⇒ ∫x3ex4 dx =∫ex4 x3 dx = ∫ey 1/4 dy

= 1/4ey + c

but y = x4, thus:

= 1/4ex4 + c