can someone solve

∫tan(x)sec^4(x)dx

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- May 6th 2010, 03:08 AMcummings15u substitution problem
can someone solve

∫tan(x)sec^4(x)dx - May 6th 2010, 03:34 AMFailure

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

$\displaystyle =-\int\frac{1}{z^5}\, dz=\ldots$ - May 6th 2010, 03:52 AMcummings15
so would it equal

sec^4(x)/4 + C - May 6th 2010, 03:58 AMFailure
Yes, you can also check it on Wolfram's "Integrator": Wolfram Mathematica Online Integrator

- May 6th 2010, 04:05 AMcummings15
thanks