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How to use it?
- Integral of d{x}:
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Integral of x^2*e^(x*(-2))
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Integral of (x^3+1)^1/2
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Integral of 1/(1+sqrt(x+1))
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Integral of xe^((x^2+2x)/2)
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Identical expressions
- xe^((x^ two + two x)/2)
- xe to the power of ((x squared plus 2x) divide by 2)
- xe to the power of ((x to the power of two plus two x) divide by 2)
- xe((x2+2x)/2)
- xex2+2x/2
- xe^((x²+2x)/2)
- xe to the power of ((x to the power of 2+2x)/2)
- xe^x^2+2x/2
- xe^((x^2+2x) divide by 2)
- xe^((x^2+2x)/2)dx
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Similar expressions
- xe^((x^2-2x)/2)
Integral of xe^((x^2+2x)/2) dx
The solution
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[src]
1 / | | 2 | x + 2*x | -------- | 2 | x*E dx | / 0
$$\int\limits_{0}^{1} e^{\frac{x^{2} + 2 x}{2}} x\, dx$$
Integral(x*E^((x^2 + 2*x)/2), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 2 2 / ___ ___\ | x + 2*x x ___ ____ |\/ 2 x*\/ 2 | -1/2 | -------- -- \/ 2 *\/ pi *erfi|----- + -------|*e | 2 x 2 \ 2 2 / | x*E dx = C + e *e - ---------------------------------------- | 2 /
$$\int e^{\frac{x^{2} + 2 x}{2}} x\, dx = C + e^{x} e^{\frac{x^{2}}{2}} - \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2} \right)}}{2 e^{\frac{1}{2}}}$$
The graph
The answer
[src]
/ ___\
___ ____ |\/ 2 | -1/2
\/ 2 *\/ pi *erfi|-----|*e ___ ____ / ___\ -1/2
\ 2 / \/ 2 *\/ pi *erfi\\/ 2 /*e 3/2
-1 + ------------------------------ - ------------------------------ + e
2 2
$$- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\sqrt{2} \right)}}{2 e^{\frac{1}{2}}} - 1 + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{2}}{2} \right)}}{2 e^{\frac{1}{2}}} + e^{\frac{3}{2}}$$
=
=
/ ___\
___ ____ |\/ 2 | -1/2
\/ 2 *\/ pi *erfi|-----|*e ___ ____ / ___\ -1/2
\ 2 / \/ 2 *\/ pi *erfi\\/ 2 /*e 3/2
-1 + ------------------------------ - ------------------------------ + e
2 2
$$- \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\sqrt{2} \right)}}{2 e^{\frac{1}{2}}} - 1 + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{2}}{2} \right)}}{2 e^{\frac{1}{2}}} + e^{\frac{3}{2}}$$
-1 + sqrt(2)*sqrt(pi)*erfi(sqrt(2)/2)*exp(-1/2)/2 - sqrt(2)*sqrt(pi)*erfi(sqrt(2))*exp(-1/2)/2 + exp(3/2)
The graph
Use the examples entering the upper and lower limits of integration.