hi!
How can I start with this integral
tanx/cos x^2 dx
thanks
A couple options. I will do one to completion (a way that I suspect they do not want you to do), and will get you started on the way I'd imagine they want you to do this:
1st Method -
$\displaystyle \int \frac{tan(x)dx}{cos^{2}(x)}\Rightarrow$
$\displaystyle =\int \frac{sin(x)dx}{cos^{3}(x)}$
Make the substitution:
$\displaystyle u=cos(x); -du=sin(x)dx$
$\displaystyle =\int \frac{sin(x)dx}{cos^{3}(x)} \Rightarrow -\int \frac{du}{u^{3}}$
$\displaystyle =\frac{1}2{u^2}$
$\displaystyle =\frac{1}{2cos^{2}(x)}$
The second method begins much in the same way by rewritting the integral:
$\displaystyle \int \frac{tan(x)dx}{cos^{2}(x)}\Rightarrow$
$\displaystyle \int \frac{tan(x)sec(x)dx}{cos(x)}$
See if you can take it from there.