What is \int ( 4x ^ { 3} + \cos x ) d x(4x3+cosx)dx?

1 Answer
Feb 7, 2018

x^4+sinxx4+sinx

Explanation:

inta+ba+b = int aa+intbb
int4x^3dx4x3dx++intcosxdxcosxdx
use the reverse power rule to integrate 4x^34x3
intmx^nmxn=int(mx^(n+1))/(n+1)mxn+1n+1
since d/dx sinx=cosxddxsinx=cosx, you can reverse it to integrate cosxcosx
so, int4x^3dx4x3dx++intcosxdxcosxdx
= 4(x^4)/44x44+sinxsinx
= x^4+sinxx4+sinx