What is the integral of int x/ cos^2(x)dx?

1 Answer
May 29, 2018

intx/(cos²(x))dx=xtan(x)+ln(|cos(x)|)+C, C in RR

Explanation:

intx/(cos²(x))dx=intx*1/(cos²(x))dx
Using integration by parts :
f(x)=x
f'(x)=1
g'(x)=1/(cos²x)
g(x)=tan(x)
So: intx/(cos²(x))dx=xtan(x)-inttan(x)dx
=xtan(x)-intsin(x)/cos(x)dx
Let X=cos(x)
dX=-sin(x)dx
So:
intx/(cos²(x))dx=xtan(x)+int1/XdX
intx/(cos²(x))dx=xtan(x)+ln(|X|)
intx/(cos²(x))dx=xtan(x)+ln(|cos(x)|)+C, C in RR
\0/ here's our answer!