Mister Exam

Other calculators

Solving integrals/ 1/sinx+sqrt^3x

Integral of 1/sinx+sqrt^3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                       
  /                       
 |                        
 |  /                3\   
 |  |    1        ___ |   
 |  |1*------ + \/ x  | dx
 |  \  sin(x)         /   
 |                        
/                         
0
$$\int\limits_{0}^{1} \left(\left(\sqrt{x}\right)^{3} + 1 \cdot \frac{1}{\sin{\left(x \right)}}\right)\, dx$$
Simplify
The answer (Indefinite) [src] 
  /                                                                        
 |                                                                         
 | /                3\                                                  5/2
 | |    1        ___ |          log(-1 + cos(x))   log(1 + cos(x))   2*x   
 | |1*------ + \/ x  | dx = C + ---------------- - --------------- + ------
 | \  sin(x)         /                 2                  2            5   
 |                                                                         
/
$$-{{\log \left(\cos x+1\right)}\over{2}}+{{\log \left(\cos x-1 \right)}\over{2}}+{{2\,x^{{{5}\over{2}}}}\over{5}}$$
Simplify
The answer [src] 
     pi*I
oo + ----
      2
$${\it \%a}$$ 
=
= 
     pi*I
oo + ----
      2
$$\infty + \frac{i \pi}{2}$$
Simplify
Numerical answer [src] 
44.5790108686112
44.5790108686112

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

    © Mister Exam – Calculator