Solving $\int_0^ {\infty}x^3e^ {-x^2}dx$ [duplicate]
Sep 9, 2024 · You used a substitution, and then integration by parts once. But what if you start out with integration by parts? $$ \begin {align} \int x^3e^ {-x^2}\,dx &=\int -\frac12x^2\left (-2xe^ { …
Find the general solution to $xy' = 2y + x^3e^x$
Nov 7, 2021 · Find the general solution to $xy' = 2y + x^3e^x$ Ask Question Asked 4 years, 5 months ago Modified 4 years, 5 months ago
calculus - Integration by Parts Question: Integrate $x^3e^x ...
Aug 14, 2015 · A nice and quick way to visualize integration by parts (it could be a time-saver!): $$\matrix {&\text {differentiate}&&& &\text {integrate}&\\ &x^3&&&&e^x ...
Solving the integral $\int r^3e^ {-r^2}$ using variable change
Aug 17, 2017 · We have the following integral: $\int r^3e^ {-r^2} dr$ from $0$ to $\sqrt2$ Normally you would solve this by partial integration, but upon attempting this I get very complex calculations.
Problems finding particular solution for $y''-4y'+4y=x+3e^{2x}$
Dec 14, 2019 · You can reach the gereral solution by integrating the given ODE repeatedly. Indeed, one has \begin {align*} & y'' - 4y' + 4 = x + 3e^ {2x} \Longleftrightarrow (y ...
If the Wronskian W of $f$ and $g$ is $3e^{4t}$, and if $f(t) = e^{2t ...
If you simplify by factoring out $e^ {2t}$ and cancelling, that would give you $$g' - 2g = 3e^ {2t},$$ instead of $g'-2g = 3e^ {4t}$, which is what you had. So it looks like you made a simplification error.
Proving $E [X^4]=3σ^4$ - Mathematics Stack Exchange
Sep 7, 2016 · Given a random variable $X\\sim\\mathcal N(0,\\sigma^2)$, how can we prove that $E[X^4]=3\\sigma^4$? I am having trouble even starting with the proof.
Evaluate: $\int\frac {3e^ {2x}-2e^x} {e^ {2x}+2e^x-8}dx$
Feb 21, 2023 · Evaluate: $\int\frac {3e^ {2x}-2e^x} {e^ {2x}+2e^x-8}dx$ Ask Question Asked 3 years, 1 month ago Modified 1 year, 5 months ago
Conditional probability in Poisson distribution
Oct 19, 2021 · The number of accidents that a person has in a given year is a Poisson random variable with mean $\\lambda$. However we may suppose that the rate $\\lambda$ depends on the person or …
Sum of Sinusoids with Same Frequency = Sinusoid (proof)
Nov 25, 2014 · I am studying Fourier analysis on my own, I realised that probably the first thing you want to proof in Fourier transform is that the sum of 2 sinuoids (namely a sine and cosine) with the same …