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Solving integrals/ a/(sin(x)*tan(x))

Integral of a/(sin(x)*tan(x)) dx

Limits of integration:

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The solution

You have entered [src] 
  1                 
  /                 
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 |        a         
 |  ------------- dx
 |  sin(x)*tan(x)   
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0
∫01asin⁡(x)tan⁡(x) dx\int\limits_{0}^{1} \frac{a}{\sin{\left(x \right)} \tan{\left(x \right)}}\, dx 
Integral(a/((sin(x)*tan(x))), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫asin⁡(x)tan⁡(x) dx=a∫1sin⁡(x)tan⁡(x) dx\int \frac{a}{\sin{\left(x \right)} \tan{\left(x \right)}}\, dx = a \int \frac{1}{\sin{\left(x \right)} \tan{\left(x \right)}}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      −1sin⁡(x)- \frac{1}{\sin{\left(x \right)}}

    So, the result is: −asin⁡(x)- \frac{a}{\sin{\left(x \right)}}

  2. Add the constant of integration:

    −asin⁡(x)+constant- \frac{a}{\sin{\left(x \right)}}+ \mathrm{constant}

The answer is:

−asin⁡(x)+constant- \frac{a}{\sin{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                              
 |       a                  a   
 | ------------- dx = C - ------
 | sin(x)*tan(x)          sin(x)
 |                              
/
∫asin⁡(x)tan⁡(x) dx=C−asin⁡(x)\int \frac{a}{\sin{\left(x \right)} \tan{\left(x \right)}}\, dx = C - \frac{a}{\sin{\left(x \right)}}
Simplify
The answer [src] 
               a   
oo*sign(a) - ------
             sin(1)
−asin⁡(1)+∞sign⁡(a)- \frac{a}{\sin{\left(1 \right)}} + \infty \operatorname{sign}{\left(a \right)} 
=
= 
               a   
oo*sign(a) - ------
             sin(1)
−asin⁡(1)+∞sign⁡(a)- \frac{a}{\sin{\left(1 \right)}} + \infty \operatorname{sign}{\left(a \right)} 
oo*sign(a) - a/sin(1)

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

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