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Nov 7, 2021 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,

Aug 14, 2015 · A nice and quick way to visualize integration by parts (it could be a time-saver!): $$\matrix {&\text {differentiate}&&& &\text {integrate}&\\ &x^3&&&&e^x ...

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Feb 3, 2016 · I have to evaluate the integral $\int_ {0}^ {\infty}t^3e^ {-3t}dt$ using complex analysis techniques (the laplace transform). Can you check my steps, please? $$\int_ {0}^ …

I need to find the value of $\displaystyle \int _0^ {2\pi}\sin^2 \left (\frac {-\pi} {6}+3e^ {it} \right)dt$. I figured I could use contour integration and the Cauchy-Goursat theorem to do so.

Dec 14, 2019 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,

Sep 9, 2024 · You used a substitution, and then integration by parts once. But what if you start out with integration by parts? $$ \begin {align} \int x^3e^ {-x^2}\,dx &=\int -\frac12x^2\left (-2xe^ { …

Feb 21, 2023 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,

Oct 2, 2020 · Is $y'''-3e^ty''- y'=t$ a linear differential equation or a nonlinear differential equation? I know the distinction between a linear D.E and nonlinear D.E but I am confused about this …