Mister Exam

Other calculators

tg(3x)^2
Solving integrals/ tg(3x)^2

Integral of tg(3x)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |     2        
 |  tan (3*x) dx
 |              
/               
0
∫01tan⁡2(3x) dx\int\limits_{0}^{1} \tan^{2}{\left(3 x \right)}\, dx 
Integral(tan(3*x)^2, (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

    tan⁡2(3x)=sec⁡2(3x)−1\tan^{2}{\left(3 x \right)} = \sec^{2}{\left(3 x \right)} - 1

  2. Integrate term-by-term:

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

      But the integral is

      sin⁡(3x)3cos⁡(3x)\frac{\sin{\left(3 x \right)}}{3 \cos{\left(3 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⁡(3x)3cos⁡(3x)- x + \frac{\sin{\left(3 x \right)}}{3 \cos{\left(3 x \right)}}

  3. Now simplify:

    −x+tan⁡(3x)3- x + \frac{\tan{\left(3 x \right)}}{3}

  4. Add the constant of integration:

    −x+tan⁡(3x)3+constant- x + \frac{\tan{\left(3 x \right)}}{3}+ \mathrm{constant}

The answer is:

−x+tan⁡(3x)3+constant- x + \frac{\tan{\left(3 x \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                                  
 |    2                    sin(3*x) 
 | tan (3*x) dx = C - x + ----------
 |                        3*cos(3*x)
/
∫tan⁡2(3x) dx=C−x+sin⁡(3x)3cos⁡(3x)\int \tan^{2}{\left(3 x \right)}\, dx = C - x + \frac{\sin{\left(3 x \right)}}{3 \cos{\left(3 x \right)}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-2000020000
Plot the graph f(x)
The answer [src] 
oo
∞\infty 
=
= 
oo
∞\infty 
oo
Numerical answer [src] 
1605.32063557435
1605.32063557435
The graph
Integral of tg(3x)^2 dx

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

    © Mister Exam – Calculator