can someone solve
∫tan(x)sec^4(x)dx
Consider this
$\displaystyle \int \tan(x)\sec^4(x)\, dx = \int \frac{\sin(x)}{\cos(x)}\cdot\frac{1}{\cos^4(x)}\, dx=-\int \frac{1}{\cos^5(x)}\cdot (-\sin(x))\,dx$
Now substitute $\displaystyle z := \cos(x)$, thus $\displaystyle dz= -\sin(x)dx$, which gives you
$\displaystyle =-\int\frac{1}{z^5}\, dz=\ldots$
Yes, you can also check it on Wolfram's "Integrator": Wolfram Mathematica Online Integrator