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

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Answer 1 · 2018-02-22T22:23:37

Look below

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?

#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#