Can you solve this integral?

I need help with the following:

4. z^2 / (5 + 5z^3)

I appreciate your time.

1 Answer

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  • 1 decade ago
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    Let u = z^3 --> du = 3z^2dz

    z^2 dz/(5 + 5z^3) = (1/5)z^2 dz/(1 + z^3)

    z^2 dz/(5 + 5z^3) = (1/5)(1/3)3z^2 dz/(1 + z^3)

    z^2 dz/(5 + 5z^3) = (1/15) du/(1 + u)

    Now integrate

    integral of z^2 dz/(5 + 5z^3) = (1/15)ln(1 + u) + C

    integral of z^2 dz/(5 + 5z^3) = (1/15)ln(1 + z^3) + C

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