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mpj4
 one year ago
does squaring a rational expression inside an integral affect dx?
mpj4
 one year ago
does squaring a rational expression inside an integral affect dx?

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mpj4
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433407624358:dwI plan to do it on a problem that looks like this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Try something like \[I= \int\limits \frac{x^2dx}{\sqrt{x^24x+5}}\]\[I=(\int\limits \frac{(x^24x+5+4x5)dx}{\sqrt{x^24x+5}})\]\[I=(\int\limits \frac{(x^24x+5)dx}{\sqrt{x^24x+5}}+4\int\limits \frac{xdx}{\sqrt{x^24x+5}}5\int\limits \frac{dx}{\sqrt{x^24x+5}})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First integral factorize in the form of \[a^2(x+z)^2\] substitute x+z so it becomes \[a^2t^2\] Use the formula \[\int\limits \sqrt{a^2t^2} dt=\frac{t \sqrt{a^2t^2}}{2}+\frac{a^2}{2}\sin^{1}(\frac{t}{a})\] Second integral Let \[x=A \frac{d(x^24x+5)}{dx}+B\] Equate coefficients and solve Third Integral Factorize and apply \[I=\int\limits \frac{dt}{\sqrt{a^2t^2}}=\sin^{1}\frac{t}{a}\]

mpj4
 one year ago
Best ResponseYou've already chosen the best response.0So sorry, I was solving other problems and skipped this one. Thank you so much
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