Question

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

Answer 1

`x^4+sinx`

Explanation:

`inta+b` = `int a`+`intb`
`int4x^3dx` `+` `intcosxdx`
use the reverse power rule to integrate `4x^3`
`intmx^n`=`int(mx^(n+1))/(n+1)`
since `d/dx sinx=cosx`, you can reverse it to integrate `cosx`
so, `int4x^3dx` `+` `intcosxdx`
= `4(x^4)/4`+`sinx`
= `x^4+sinx`