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Integration help? C4

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Reply 1
Original post by 1017bsquad
Need real quick help on how to integrate this? http://prntscr.com/b9yqrq


Use the substitution u=x3u =x^3 if you can't do it by recognition.
Reply 2
Worth pointing out I think that we can get the integration into the form g(x)fg(x)dx\int g'(x)fg(x) dx and then use
g(x)fg(x)dx=fg(x)dg(x)\int g'(x)fg(x) dx=\int fg(x) dg(x)
by doing
x2(x3+1)3  dx=133x2(x3+1)3  dx=13(x3+1)3d(x3+1)=13(x3+1)44+c\int x^2 (x^3+1)^3\;dx = \frac{1}{3} \int 3x^2 (x^3+1)^3\;dx =\frac{1}{3}\int(x^3+1)^3 d(x^3+1)=\frac{1}{3}\frac{(x^3+1)^4}{4}+c

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