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Solving integrals/ sqrt(x)*(ln(x))^3

Integral of sqrt(x)*(ln(x))^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |    ___    3      
 |  \/ x *log (x) dx
 |                  
/                   
0
∫01xlog⁡(x)3 dx\int\limits_{0}^{1} \sqrt{x} \log{\left(x \right)}^{3}\, dx 
Integral(sqrt(x)*log(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                 
 |                            3/2      3/2    2         3/2    3          3/2       
 |   ___    3             32*x      4*x   *log (x)   2*x   *log (x)   16*x   *log(x)
 | \/ x *log (x) dx = C - ------- - -------------- + -------------- + --------------
 |                           27           3                3                9       
/
∫xlog⁡(x)3 dx=C+2x32log⁡(x)33−4x32log⁡(x)23+16x32log⁡(x)9−32x3227\int \sqrt{x} \log{\left(x \right)}^{3}\, dx = C + \frac{2 x^{\frac{3}{2}} \log{\left(x \right)}^{3}}{3} - \frac{4 x^{\frac{3}{2}} \log{\left(x \right)}^{2}}{3} + \frac{16 x^{\frac{3}{2}} \log{\left(x \right)}}{9} - \frac{32 x^{\frac{3}{2}}}{27}
Simplify
The answer [src] 
-32 
----
 27
−3227- \frac{32}{27} 
=
= 
-32 
----
 27
−3227- \frac{32}{27} 
-32/27
Numerical answer [src] 
-1.18518518518519
-1.18518518518519

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

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