Mister Exam

Other calculators

Solving integrals/ sinx*ln(tanx)

Integral of sinx*ln(tanx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                      
  /                      
 |                       
 |  sin(x)*log(tan(x)) dx
 |                       
/                        
0
$$\int\limits_{0}^{1} \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\, dx$$ 
Integral(sin(x)*log(tan(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                   
 |                             log(-1 + cos(x))   log(1 + cos(x))                     
 | sin(x)*log(tan(x)) dx = C + ---------------- - --------------- - cos(x)*log(tan(x))
 |                                    2                  2                            
/
$$\int \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\, dx = C + \frac{\log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{2} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}$$
Simplify
Numerical answer [src] 
-0.150801464774004
-0.150801464774004

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

    © Mister Exam – Calculator