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Math Help - integration problems

  1. #1
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    integration problems

    I'm not sure how to sort out the following:

    1. integrationOf (3 + sqrtOf(2x + 5))

    Answer: ?

    2. integrationOf( e^7x-4) dx
    limits 1 to 3

    Answer: (e^7x-4/7)
    limits 1 to 3

    3. integrationOf((5-3x)^-1) dx
    limits 0 to 1

    Answer: ?

    p.s. what are the tags to use to draw the actual characters? any docs around here?
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  2. #2
    o_O
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    #1:
    \int \left( 3 + \sqrt{2x + 5}\right) dx \: \: = \: \: \int 3 \: dx + \int \sqrt{2x + 5} \: dx

    Imagine x^{0} in front of the 3 for the first integral and use the substitution  u = 2x + 5 \: \: \Rightarrow \: \: du = 2 dx for your right.

    #2:
    \int_{1}^{3} e^{7x - 4} \: dx

    Use: u = 7x - 4. Don't forget to change your limits on your integrand accordingly.

    #3:
    \int_{0}^{1} (5-3x)^{-1} \: dx

    Use u = 5 - 3x \: \: \Rightarrow \: \: du = -3dx for your sub. This gives you: \int_{u(0)}^{u(1)} u^{-1} \frac{du}{-3} = -\frac{1}{3}\int_{5}^{2} u^{-1} \:du

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