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(2/cos²x-3sin²x)dx

Integral of (2/cos²x-3sin²x)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                         
  /                         
 |                          
 |  /   2           2   \   
 |  |------- - 3*sin (x)| dx
 |  |   2               |   
 |  \cos (x)            /   
 |                          
/                           
0                           
$$\int\limits_{0}^{1} \left(- 3 \sin^{2}{\left(x \right)} + \frac{2}{\cos^{2}{\left(x \right)}}\right)\, dx$$
Integral(2/cos(x)^2 - 3*sin(x)^2, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Rewrite the integrand:

      2. Integrate term-by-term:

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

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. Let .

            Then let and substitute :

            1. The integral of a constant times a function is the constant times the integral of the function:

              1. The integral of cosine is sine:

              So, the result is:

            Now substitute back in:

          So, the result is:

        The result is:

      So, the result is:

    1. The integral of a constant times a function is the constant times the integral of the function:

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

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                          
 |                                                           
 | /   2           2   \          3*x   3*sin(2*x)   2*sin(x)
 | |------- - 3*sin (x)| dx = C - --- + ---------- + --------
 | |   2               |           2        4         cos(x) 
 | \cos (x)            /                                     
 |                                                           
/                                                            
$$\int \left(- 3 \sin^{2}{\left(x \right)} + \frac{2}{\cos^{2}{\left(x \right)}}\right)\, dx = C - \frac{3 x}{2} + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{3 \sin{\left(2 x \right)}}{4}$$
The graph
The answer [src]
  3   2*sin(1)   3*cos(1)*sin(1)
- - + -------- + ---------------
  2    cos(1)           2       
$$- \frac{3}{2} + \frac{3 \sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
=
=
  3   2*sin(1)   3*cos(1)*sin(1)
- - + -------- + ---------------
  2    cos(1)           2       
$$- \frac{3}{2} + \frac{3 \sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
-3/2 + 2*sin(1)/cos(1) + 3*cos(1)*sin(1)/2
Numerical answer [src]
2.29678851942907
2.29678851942907
The graph
Integral of (2/cos²x-3sin²x)dx dx

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