Integral of arccos(x)*exp((a*x)) dx
The solution
The answer (Indefinite)
[src]
// ________ \
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|| -\/ 1 - x for a = 0|
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/ // x for a = 0\ || | |
| || | || | a*x |
| a*x || a*x | || | e |
| acos(x)*e dx = C + |
$$\int e^{a x} \operatorname{acos}{\left(x \right)}\, dx = C + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \operatorname{acos}{\left(x \right)} + \begin{cases} - \sqrt{1 - x^{2}} & \text{for}\: a = 0 \\\frac{\int \frac{e^{a x}}{\sqrt{1 - x^{2}}}\, dx}{a} & \text{otherwise} \end{cases}$$
pi
/
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| a*x
| acos(x)*e dx
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/
-pi
$$\int\limits_{- \pi}^{\pi} e^{a x} \operatorname{acos}{\left(x \right)}\, dx$$
=
pi
/
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| a*x
| acos(x)*e dx
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/
-pi
$$\int\limits_{- \pi}^{\pi} e^{a x} \operatorname{acos}{\left(x \right)}\, dx$$
Integral(acos(x)*exp(a*x), (x, -pi, pi))
Use the examples entering the upper and lower limits of integration.