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tan^2(5x)
Solving integrals/ tan^2(5x)

Integral of tan^2(5x) dx

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The solution

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∫01tan⁡2(5x) dx\int\limits_{0}^{1} \tan^{2}{\left(5 x \right)}\, dx 
Integral(tan(5*x)^2, (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    tan⁡2(5x)=sec⁡2(5x)−1\tan^{2}{\left(5 x \right)} = \sec^{2}{\left(5 x \right)} - 1

  2. Integrate term-by-term:

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

      But the integral is

      sin⁡(5x)5cos⁡(5x)\frac{\sin{\left(5 x \right)}}{5 \cos{\left(5 x \right)}}

    1. The integral of a constant is the constant times the variable of integration:

      ∫(−1) dx=−x\int \left(-1\right)\, dx = - x

    The result is: −x+sin⁡(5x)5cos⁡(5x)- x + \frac{\sin{\left(5 x \right)}}{5 \cos{\left(5 x \right)}}

  3. Now simplify:

    −x+tan⁡(5x)5- x + \frac{\tan{\left(5 x \right)}}{5}

  4. Add the constant of integration:

    −x+tan⁡(5x)5+constant- x + \frac{\tan{\left(5 x \right)}}{5}+ \mathrm{constant}

The answer is:

−x+tan⁡(5x)5+constant- x + \frac{\tan{\left(5 x \right)}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
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 |    2                    sin(5*x) 
 | tan (5*x) dx = C - x + ----------
 |                        5*cos(5*x)
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tan⁡(5 x)−5 x5{{\tan \left(5\,x\right)-5\,x}\over{5}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90200000-100000
Plot the graph f(x)
The answer [src] 
oo
tan⁡5−55{{\tan 5-5}\over{5}} 
=
= 
oo
∞\infty
Упростить
Numerical answer [src] 
241.799578144155
241.799578144155
The graph
Integral of tan^2(5x) dx

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

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