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(tan^4)x
Solving integrals/ (tan^4)x

Integral of (tan^4)x dx

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The solution

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  1             
  /             
 |              
 |     4        
 |  tan (x)*x dx
 |              
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0
$$\int\limits_{0}^{1} x \tan^{4}{\left(x \right)}\, dx$$ 
Integral(tan(x)^4*x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                           
 |                     2      2           /       2   \                   3   
 |    4               x    tan (x)   2*log\1 + tan (x)/              x*tan (x)
 | tan (x)*x dx = C + -- - ------- + ------------------ - x*tan(x) + ---------
 |                    2       6              3                           3    
/
$$\int x \tan^{4}{\left(x \right)}\, dx = C + \frac{x^{2}}{2} + \frac{x \tan^{3}{\left(x \right)}}{3} - x \tan{\left(x \right)} + \frac{2 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{3} - \frac{\tan^{2}{\left(x \right)}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                2         3           /       2   \
1            tan (1)   tan (1)   2*log\1 + tan (1)/
- - tan(1) - ------- + ------- + ------------------
2               6         3              3
$$- \tan{\left(1 \right)} - \frac{\tan^{2}{\left(1 \right)}}{6} + \frac{1}{2} + \frac{2 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{3} + \frac{\tan^{3}{\left(1 \right)}}{3}$$ 
=
= 
                2         3           /       2   \
1            tan (1)   tan (1)   2*log\1 + tan (1)/
- - tan(1) - ------- + ------- + ------------------
2               6         3              3
$$- \tan{\left(1 \right)} - \frac{\tan^{2}{\left(1 \right)}}{6} + \frac{1}{2} + \frac{2 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{3} + \frac{\tan^{3}{\left(1 \right)}}{3}$$ 
1/2 - tan(1) - tan(1)^2/6 + tan(1)^3/3 + 2*log(1 + tan(1)^2)/3
Numerical answer [src] 
0.618348348334909
0.618348348334909
The graph
Integral of (tan^4)x dx

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

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