Selesaikan ∫ (from - pi / 2 to 2 pi) of e^xx^3 wrt x

Nilaikan

\frac{\pi ^{2}\left(\pi e^{\frac{\pi }{2}}+6e^{\frac{\pi }{2}}-96e^{3\pi }\right)+24\left(\pi +2\right)e^{\frac{\pi }{2}}+64\pi ^{3}e^{3\pi }+96\pi e^{3\pi }-48e^{3\pi }}{8e^{\pi }}\approx 86387.890687341

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Integration

5 masalah yang serupa dengan:

\int _ { - \pi / 2 } ^ { 2 \pi } e ^ { x } x ^ { 3 } d x

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Determine whether it is convergent or divergent: \int_{-1}^0 {\frac{e^{1/x}}{x^3}}dx

https://math.stackexchange.com/questions/1183236/determine-whether-it-is-convergent-or-divergent-int-10-frace1-xx

Notice that the 0 in “ \dfrac10 ” is slightly negative, so we are actually dealing with \displaystyle\lim_{x\to0^-}e^{1/x}\bigg(1-\frac1x\bigg), where the first part goes towards e^{-\infty}=0 ...

Hint for integration \int_{-2}^{2} \frac{3x^2}{1+e^x}\mathrm dx

https://math.stackexchange.com/q/2320427

Let u=-x. \begin{align} \int_{-2}^2\frac{3x^2}{1+e^x}dx&=\int_2^{-2}\frac{-3u^2}{1+e^{-u}}du\\ &=\int_{-2}^2\frac{3u^2}{1+e^{-u}}du\\ &=\int_{-2}^2\frac{3u^2e^u}{1+e^{u}}du\\ ...

Evaluating \int_{-1}^{1} \frac{dx}{(e^x+1)(x^2+1)} [duplicate]

https://math.stackexchange.com/questions/1805550/evaluating-int-11-fracdxex1x21

Hint . One may write \begin{align} \int_{-1}^{1} \frac{dx}{(e^x+1)(x^2+1)} &=\int_{-1}^0 \frac{dx}{(e^x+1)(x^2+1)} +\int_0^{1} \frac{dx}{(e^x+1)(x^2+1)} \\\\&=\int_0^1 \frac{dx}{(e^{-x}+1)(x^2+1)} +\int_0^{1} \frac{dx}{(e^x+1)(x^2+1)} \\\\&=\int_0^1 \frac{e^x\:dx}{(e^{x}+1)(x^2+1)} +\int_0^{1} \frac{dx}{(e^x+1)(x^2+1)} \\\\&=\int_0^1 \frac{(e^x+1)\:dx}{(e^{x}+1)(x^2+1)} \\\\&=\int_0^1 \frac{dx}{(x^2+1)} \end{align} ...

How I can evaluate this integral?

https://math.stackexchange.com/q/2913032

\begin{align} \int_{-\pi}^{\pi}e^{\frac{-|x|^2}{t}}\theta(t)dx &=\theta(t)\int^\pi_{-\pi}e^{-x^2/t}dx \\ &=\theta(t)\int^\pi_{-\pi}e^{-(x/\sqrt t)^2}dx \\ &=\theta(t)\int^{\pi/\sqrt t}_{-\pi/\sqrt t}e^{-u^2}\sqrt t~du \qquad{(1)}\\ &=\theta(t)\sqrt t\int^{\pi/\sqrt t}_{-\pi/\sqrt t}e^{-u^2}du \\ &=\theta(t)\sqrt t\sqrt \pi\operatorname{erf}\left(\frac{\pi}{\sqrt t}\right) \qquad{(2)}\\ \end{align} ...

AP Calculus Fundamental Theorem of Calculus

https://math.stackexchange.com/q/2785698

First off, I'm assuming that you want to evaluate this: \frac{d}{dx} \int_2^{x^2}e^{t^3}dt You want to find the derivative of the integral, so we replace the x inside the integral with a dummy ...

Energy for the 1D Heat Equation

https://math.stackexchange.com/q/655210

Hint. Using integration by parts we obtain that \int_0^L u(x,t)u_{xx}(x,t)\,dx=u(x,t)u_{x}(x,t)\,\big|_0^L-\int_0^L u_{x}^2(x,t)\,dx.

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Persamaan kuadratik

{ x } ^ { 2 } - 4 x - 5 = 0

Trigonometri

4 \sin \theta \cos \theta = 2 \sin \theta

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

Persamaan serentak

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

Pembezaan

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

Pengamiran

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

Had

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

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