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sin(x)tan^3(x)
Solving integrals/ sin(x)tan^3(x)

Integral of sin(x)tan^3(x) dx

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The solution

You have entered [src] 
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∫01sin⁡(x)tan⁡3(x) dx\int\limits_{0}^{1} \sin{\left(x \right)} \tan^{3}{\left(x \right)}\, dx 
Integral(sin(x)*tan(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
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 |           3             3*log(1 + sin(x))   3*log(-1 + sin(x))       sin(x)             
 | sin(x)*tan (x) dx = C - ----------------- + ------------------ - -------------- + sin(x)
 |                                 4                   4                      2            
/                                                                   -2 + 2*sin (x)
∫sin⁡(x)tan⁡3(x) dx=C+3log⁡(sin⁡(x)−1)4−3log⁡(sin⁡(x)+1)4+sin⁡(x)−sin⁡(x)2sin⁡2(x)−2\int \sin{\left(x \right)} \tan^{3}{\left(x \right)}\, dx = C + \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{4} + \sin{\left(x \right)} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
  3*log(1 + sin(1))   3*log(1 - sin(1))       sin(1)             
- ----------------- + ----------------- - -------------- + sin(1)
          4                   4                     2            
                                          -2 + 2*sin (1)
3log⁡(1−sin⁡(1))4−3log⁡(sin⁡(1)+1)4+sin⁡(1)−sin⁡(1)−2+2sin⁡2(1)\frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} + \sin{\left(1 \right)} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}} 
=
= 
  3*log(1 + sin(1))   3*log(1 - sin(1))       sin(1)             
- ----------------- + ----------------- - -------------- + sin(1)
          4                   4                     2            
                                          -2 + 2*sin (1)
3log⁡(1−sin⁡(1))4−3log⁡(sin⁡(1)+1)4+sin⁡(1)−sin⁡(1)−2+2sin⁡2(1)\frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} + \sin{\left(1 \right)} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}} 
-3*log(1 + sin(1))/4 + 3*log(1 - sin(1))/4 - sin(1)/(-2 + 2*sin(1)^2) + sin(1)
Numerical answer [src] 
0.443421576297111
0.443421576297111
The graph
Integral of sin(x)tan^3(x) dx

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

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