# Math Help - u substitution problem

1. ## u substitution problem

can someone solve

∫tan(x)sec^4(x)dx

2. Originally Posted by cummings15
can someone solve

∫tan(x)sec^4(x)dx

Consider this

$\int \tan(x)\sec^4(x)\, dx = \int \frac{\sin(x)}{\cos(x)}\cdot\frac{1}{\cos^4(x)}\, dx=-\int \frac{1}{\cos^5(x)}\cdot (-\sin(x))\,dx$

Now substitute $z := \cos(x)$, thus $dz= -\sin(x)dx$, which gives you

$=-\int\frac{1}{z^5}\, dz=\ldots$

3. so would it equal

sec^4(x)/4 + C

4. Originally Posted by cummings15
so would it equal

sec^4(x)/4 + C
Yes, you can also check it on Wolfram's "Integrator": Wolfram Mathematica Online Integrator

5. thanks