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Math Help - 2 indefinite integration probs using u substitution

  1. #1
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    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
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by calvin_coolidge View Post
    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
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