Mister Exam

Other calculators

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                   
$$\int\limits_{0}^{1} \sqrt{x} \log{\left(x \right)}^{3}\, dx$$
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       
/                                                                                   
$$\int \sqrt{x} \log{\left(x \right)}^{3}\, dx = C + \frac{2 x^{\frac{3}{2}} \log{\left(x \right)}^{3}}{3} - \frac{4 x^{\frac{3}{2}} \log{\left(x \right)}^{2}}{3} + \frac{16 x^{\frac{3}{2}} \log{\left(x \right)}}{9} - \frac{32 x^{\frac{3}{2}}}{27}$$
The answer [src]
-32 
----
 27 
$$- \frac{32}{27}$$
=
=
-32 
----
 27 
$$- \frac{32}{27}$$
-32/27
Numerical answer [src]
-1.18518518518519
-1.18518518518519

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