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Solving integrals/ a^(3logx)dx

Integral of a^(3logx)dx dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |   3*log(x)   
 |  a         dx
 |              
/               
0
$$\int\limits_{0}^{1} a^{3 \log{\left(x \right)}}\, dx$$ 
Integral(a^(3*log(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                   //   3*log(x)                 \
 |                    ||x*a                     -1/3|
 |  3*log(x)          ||------------  for a != e    |
 | a         dx = C + |<1 + 3*log(a)                |
 |                    ||                            |
/                     ||   log(x)       otherwise   |
                      \\                            /
$$\int a^{3 \log{\left(x \right)}}\, dx = C + \begin{cases} \frac{a^{3 \log{\left(x \right)}} x}{3 \log{\left(a \right)} + 1} & \text{for}\: a \neq e^{- \frac{1}{3}} \\\log{\left(x \right)} & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
  1             
  /             
 |              
 |   3*log(x)   
 |  a         dx
 |              
/               
0
$$\int\limits_{0}^{1} a^{3 \log{\left(x \right)}}\, dx$$ 
=
= 
  1             
  /             
 |              
 |   3*log(x)   
 |  a         dx
 |              
/               
0
$$\int\limits_{0}^{1} a^{3 \log{\left(x \right)}}\, dx$$ 
Integral(a^(3*log(x)), (x, 0, 1))

    Use the examples entering the upper and lower limits of integration.

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