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Solving integrals/ 1/(sin(x+y^2))

Integral of 1/(sin(x+y^2)) dx

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The solution

You have entered [src] 
  1               
  /               
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 |       1        
 |  ----------- dx
 |     /     2\   
 |  sin\x + y /   
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0
∫011sin⁡(x+y2) dx\int\limits_{0}^{1} \frac{1}{\sin{\left(x + y^{2} \right)}}\, dx 
Integral(1/sin(x + y^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                     
 |                         /   /     2\\
 |      1                  |   |x   y ||
 | ----------- dx = C + log|tan|- + --||
 |    /     2\             \   \2   2 //
 | sin\x + y /                          
 |                                      
/
∫1sin⁡(x+y2) dx=C+log⁡(tan⁡(x2+y22))\int \frac{1}{\sin{\left(x + y^{2} \right)}}\, dx = C + \log{\left(\tan{\left(\frac{x}{2} + \frac{y^{2}}{2} \right)} \right)}
Simplify
The answer [src] 
     /   / 2\\      /   /     2\\
     |   |y ||      |   |1   y ||
- log|tan|--|| + log|tan|- + --||
     \   \2 //      \   \2   2 //
−log⁡(tan⁡(y22))+log⁡(tan⁡(y22+12))- \log{\left(\tan{\left(\frac{y^{2}}{2} \right)} \right)} + \log{\left(\tan{\left(\frac{y^{2}}{2} + \frac{1}{2} \right)} \right)} 
=
= 
     /   / 2\\      /   /     2\\
     |   |y ||      |   |1   y ||
- log|tan|--|| + log|tan|- + --||
     \   \2 //      \   \2   2 //
−log⁡(tan⁡(y22))+log⁡(tan⁡(y22+12))- \log{\left(\tan{\left(\frac{y^{2}}{2} \right)} \right)} + \log{\left(\tan{\left(\frac{y^{2}}{2} + \frac{1}{2} \right)} \right)} 
-log(tan(y^2/2)) + log(tan(1/2 + y^2/2))

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

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