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Solving integrals/ (sqrt(x))((ln(x))/(ln(2)))

Integral of (sqrt(x))((ln(x))/(ln(2))) dx

Limits of integration:

from to
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Piecewise:

The solution

You have entered [src] 
  4                
  /                
 |                 
 |    ___ log(x)   
 |  \/ x *------ dx
 |        log(2)   
 |                 
/                  
1
∫14xlog⁡(x)log⁡(2) dx\int\limits_{1}^{4} \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx 
Integral(sqrt(x)*(log(x)/log(2)), (x, 1, 4))
The answer (Indefinite) [src] 
                           /     3/2    3/2       \
  /                        |  2*x      x   *log(x)|
 |                       2*|- ------ + -----------|
 |   ___ log(x)            \    9           3     /
 | \/ x *------ dx = C + --------------------------
 |       log(2)                    log(2)          
 |                                                 
/
∫xlog⁡(x)log⁡(2) dx=C+2(x32log⁡(x)3−2x329)log⁡(2)\int \sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\, dx = C + \frac{2 \left(\frac{x^{\frac{3}{2}} \log{\left(x \right)}}{3} - \frac{2 x^{\frac{3}{2}}}{9}\right)}{\log{\left(2 \right)}}
Simplify
The answer [src] 
             32   16*log(4)
           - -- + ---------
   4         9        3    
-------- + ----------------
9*log(2)        log(2)
49log⁡(2)+−329+16log⁡(4)3log⁡(2)\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}} 
=
= 
             32   16*log(4)
           - -- + ---------
   4         9        3    
-------- + ----------------
9*log(2)        log(2)
49log⁡(2)+−329+16log⁡(4)3log⁡(2)\frac{4}{9 \log{\left(2 \right)}} + \frac{- \frac{32}{9} + \frac{16 \log{\left(4 \right)}}{3}}{\log{\left(2 \right)}} 
4/(9*log(2)) + (-32/9 + 16*log(4)/3)/log(2)
Numerical answer [src] 
6.17828209501211
6.17828209501211

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

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