# Thread: 2 indefinite integration probs using u substitution

1. ## 2 indefinite integration probs using u substitution

1) integral [tan^2x sec^2 x] dx

2) integral (6 cos t)/(2+sin t)^3 dt

On the first, what should be u? Should I use trig identities to simplify first?

On the second, I had u=2+sin t, then du=cos t....would this be correct?

Thx,

~CC

2. Originally Posted by calvin_coolidge
1) integral [tan^2x sec^2 x] dx

2) integral (6 cos t)/(2+sin t)^3 dt

On the first, what should be u? Should I use trig identities to simplify first?

On the second, I had u=2+sin t, then du=cos t....would this be correct?

Thx,

~CC
1) Let $u=\tan(x)$ and $du=\sec^2(x)\,dx$. The integral is now $\int u^2\,du$

2) Let $u=2+\sin(t)$ and $du=\cos(t)\,dt$. The integral is now $6\int\frac{1}{u^3}\,du$