Question

having trouble evaluating integrals with trig functions in them. any help?

Answer 1

post the Q

Answer 2

\[\int\limits_{}^{} [(\sec ^{3}\theta \tan \theta) / (1+\tan ^{2}\theta)] d \theta\]

Answer 3

1+tan^2 x = sec^2 x

Answer 4

Well, first start by factoring out a secan on the top to get \[\tan^2(\theta)+1 = \sec^2(\theta)\]

Answer 5

\[\int\limits \frac{ \sec^3(\theta)\tan(\theta) }{ 1+\tan^2(\theta) }d(\theta) = \int\limits \frac{ \sec(\theta) \sec^2(\theta)\tan(\theta) }{ 1+\tan^2(\theta) }d(\theta) = \int\limits \frac{ \sec(\theta) (1+\tan^2(\theta)\tan(\theta) }{ 1+\tan^2(\theta) }d(\theta)\]

Answer 6

I'm sure you can figure out the integral easily from there.

Answer 7

Sorry, the last part of is cut out and should be:
\[= \int\limits \frac{ \sec(\theta) (1+\tan^2(\theta))\tan(\theta) }{ 1+\tan^2(\theta) }d(\theta)\]