I think I've got this, but I'm not quite sure, especially about multiplying to get du to be what I want. Can someone please tell me if this is correct? (The first line is the problem.) Thanks!(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int\frac{3xdx}{\sqrt[3]{2x^2+3}}[/tex]

I set [tex]u=2x^2+3, du=4x[/tex] so the problem becomes

[tex]\int u^{-\frac{1}{3}}(\frac{3}{4})(\frac{4}{3})3xdx[/tex]

rearranging the constants gives the much nicer equation

[tex]\frac{3}{4}\int u^{-\frac{1}{3}}du[/tex]

[tex]=(\frac{3}{4})(\frac{u^\frac{2}{3}}{\frac{2}{3}})+C[/tex]

[tex]=\frac{9(2x^2+3)^\frac{2}{3}}{8}+C[/tex]

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# Homework Help: Simple integration based on chain rule

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