Question

Is integration by parts necessary to solve ∫x4ex5?

Answer 1

No not necessary. It can be solved by method of substitution

Let x⁵ = a

da/dx = 5x⁴ ===> da/5 = x⁴dx

Now ,

∫eᵃ.da/5 = eᵃ/5

Substituting back a we get

eˣ⁵/5