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Math Help - Evaluating the integral:

  1. #1
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    Evaluating the integral:

    10x(5x^2 - 3)^4 dx


    I got it to [10x (5x^2)^5]/5

    First off, is this correct? And if so, should it be simplified?
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  2. #2
    Senior Member eumyang's Avatar
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    Not quite.

    \displaystyle \int 10x(5x^2 - 3)^4 \,dx

    \begin{aligned}<br />
u &= 5x^2 - 3 \\<br />
du &= 10x \,dx<br />
\end{aligned}

    \begin{aligned}<br />
\displaystyle \int u^4 \,du &= \dfrac{u^5}{5} + C \\<br />
&= \dfrac{1}{5}(5x^2 - 3)^5 + C<br />
\end{aligned}
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  3. #3
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    Okay, so if the 10x is already there you don't have to put it back in the problem?
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  4. #4
    Senior Member eumyang's Avatar
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    That's right, you don't.
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  5. #5
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    Okay, thanks guys. That probably explains some of my other problems. I really appreciate it.
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