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Math Help - More complex indefinite integrals by substitution

  1. #1
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    More complex indefinite integrals by substitution

    I've attached a picture with two more problems I'm working on. For the first I have no idea what to use as u because it seems differentiating any term won't give you part of another term in the problem.

    As for the second one, the fact that there's a dt in the numerator is throwing me off and I don't know what to do in problems like this.
    Attached Thumbnails Attached Thumbnails More complex indefinite integrals by substitution-picture-2.png  
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    Ok I figured out #8, anyone want to help me out with the other?
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    Quote Originally Posted by fattydq View Post
    Ok I figured out #8, anyone want to help me out with the other?
    (7) is \int (x+ 34)\sqrt{68x+ x^2}dx
    The only reasonable substitution is u= 68x+ x^2. That just happens to work nicely because du= (68+ 2x)dx= 2(34+ x)dx!
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  4. #4
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    sub. 68x+x^2=t \Rightarrow (2x+68)dx = dt which you can simplify to  (x+34)dx=\frac{dt}{2} now the integral will be \frac{1}{2}\int{t^{\frac{1}{2}}dt} = ...
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