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anonymous
 5 years ago
integrate (x)(x^21)dx by subst without first multiplying. Why not?
anonymous
 5 years ago
integrate (x)(x^21)dx by subst without first multiplying. Why not?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just to get the practice of using a usubstitution; you COULD do it by multiplying, but that's seemingly not the point.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{\infty}^{\infty}(x ^{3}x)dx\] Start by separating the terms along with the differential: \[\int\limits_{\infty}^{\infty}x ^{3}dx  \int\limits_{\infty}^{\infty}xdx\] Integrate both parts: \[(\frac{1}{4}x^4\frac{1}{2}x^2+c)^{\infty}_{\infty}\] I'm posting the above because I just took all the time to make the equations look nice in the editor, but I know realize you were not supposed to multiply first. In this case, you were asked to integrate as given to practice usubstitution as stated earlier. \[u = x^21 \] \[du = 2xdx\] \[\frac{1}{2}du=xdx\] \[\frac{1}{2}\int\limits_{\infty}^{\infty}udu\] \[(\frac{1}{2})(\frac{1}{2})u^2=\frac{1}{4}u^2+c\] Then substitute back in the value of u: \[=\frac{1}{4}(x^21)+c\]
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