I am stuck with this integral: \int\frac{dx}{(3+\cos^2 x)\cdot\tan x}

trasbocohf1

trasbocohf1

Answered question

2022-02-26

I am stuck with this integral:
dx(3+cos2x)tanx

Answer & Explanation

Kwame Malone

Kwame Malone

Beginner2022-02-27Added 5 answers

Another approach is to use cos2x=1sin2x. Write the tanx as sinxcosx. We end up with
cosx(4sin2x)sinxdx
Make the substitution u=sinx. We end up with
1(4u2)u
This is a rational function, use partial fractions. I think that our integrand is
1812u1812+u+141u
Now the integration is easy. We get
18log(4u2)+14logu+C

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