I am in standard $XI$ (i.e.11) and newbie in learning topic of integration. My friend asked me to find indefinite integral of the example shown below
$$y=\int \frac{1} {{\sin(x)+\sec^2(x)}} \, \mathrm{d}x \tag 1$$
What I tried until now is I done substitution as $m=\sin(x)$
$$\frac{\textrm{d}m}{\textrm{d}x}=\cos(x)$$
Now, converting equation $(1)$ in terms of $m$ becomes as
$$y=\int \frac{(1-m^2)^{1/2}} {{1+m(1-m^2)}} \, \mathrm{d}m$$
but as you can see that it became more complicated than original equation $(1)$
So can anybody help me to compute integration of $\int \frac{1} {\sin(x)+\sec^2(x)} \, \mathrm{d}x$ ?