How do you find the antiderivative of 3x+cosx^2?

1 Answer
Feb 22, 2018

Look below

Explanation:

First, separate these

int3xdx + int cos^2xdx

for the first integral, use the reverse power rule

\frac{nx^{n+1}}{n+1}

int 3x dx = \frac{3x^4}{4}

now, the int cos^xdx

if you remember your trig integrals, you should know intcos^2xdx = 1/2x+1/4sin2x
Why?

you use integration by parts.

intcos^nx=1/ncos^{n-1}xsinx+\frac{n-1}{n}intcos^{n-2}xdx
now to compute it.

\frac{3x^4}{4}+1/2x+1/4sin2x