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I tried two methods of doing this,

a. $\int(x^2)^ndx = \int{x^{2n}}dx = \frac {x^{2n+1}}{2n+1}+C$

b. $\int(x^2)^ndx = \frac{({x^2})^{n+1}}{(n+1)(2x)}+C = \frac {x^{2n+1}}{2n+2}+C$

why is it different?

dannis islan
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    The second method is flawed. While it is the case that $\int f(g(x))g'(x),dx = F(g(x))$ if $F$ is an antiderivative of $f$, it is not the case that $\int f(g(x)),dx = F(g(x))/g'(x)$, as you have just shown. (If that latter formula were valid, why would we ever use substitution?) – Greg Martin May 27 '22 at 02:58
  • @GregMartin, maybe your comment is better placed as an answer, very well explained by the way. – person May 27 '22 at 03:38

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