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Integral of arccos(x)*exp((a*x)) dx

Limits of integration:

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The solution

You have entered [src]
 pi                
  /                
 |                 
 |           a*x   
 |  acos(x)*e    dx
 |                 
/                  
-pi                
$$\int\limits_{- \pi}^{\pi} e^{a x} \operatorname{acos}{\left(x \right)}\, dx$$
Integral(acos(x)*exp(a*x), (x, -pi, pi))
The answer (Indefinite) [src]
                                                      //      ________              \
                                                      ||     /      2               |
                                                      ||  -\/  1 - x       for a = 0|
                                                      ||                            |
                                                      ||  /                         |
  /                      // x    for a = 0\           || |                          |
 |                       ||               |           || |      a*x                 |
 |          a*x          || a*x           |           || |     e                    |
 | acos(x)*e    dx = C + |
            
$$\int e^{a x} \operatorname{acos}{\left(x \right)}\, dx = C + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \operatorname{acos}{\left(x \right)} + \begin{cases} - \sqrt{1 - x^{2}} & \text{for}\: a = 0 \\\frac{\int \frac{e^{a x}}{\sqrt{1 - x^{2}}}\, dx}{a} & \text{otherwise} \end{cases}$$
The answer [src]
 pi                
  /                
 |                 
 |           a*x   
 |  acos(x)*e    dx
 |                 
/                  
-pi                
$$\int\limits_{- \pi}^{\pi} e^{a x} \operatorname{acos}{\left(x \right)}\, dx$$
=
=
 pi                
  /                
 |                 
 |           a*x   
 |  acos(x)*e    dx
 |                 
/                  
-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.