two calculus trig integral problems!

**holly123** · November 20th 2008, 12:50 PM

integrate tan^2(3x)sec^4(3x)dx

integrate (1+sinx)/(cos^2 x) dx

**galactus** · November 20th 2008, 01:04 PM

$\int tan^{2}(3x)sec^{4}(3x)dx$

Let $u=3x, \;\ \frac{du}{3}=dx$

$\frac{1}{3}\int tan^{2}(u)sec^{4}(u)du$

Rewrite by using the identity $sec^{2}(u)=tan^{2}(u)+1$

$\frac{1}{3}\int sec^{2}(u)tan^{2}(u)du+\frac{1}{3}\int tan^{4}(u)sec^{2}(u)du$

Now, a simple sub and it works out well to finish.

Let $w=tan(u), \;\ dw=sec^{2}(u)du$

Then, resub.

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