Mister Exam

Integral of cos3xsin2xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                     
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 |  cos(3*x)*sin(2*x) dx
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$$\int\limits_{0}^{\frac{\pi}{2}} \sin{\left(2 x \right)} \cos{\left(3 x \right)}\, dx$$
Integral(cos(3*x)*sin(2*x), (x, 0, pi/2))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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 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 is when :

              So, the result is:

            Now substitute back in:

          So, the result is:

        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 is when :

              So, the result is:

            Now substitute back in:

          So, the result is:

        The result is:

      So, the result is:

    Method #2

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      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 is when :

            So, the result is:

          Now substitute back in:

        So, the result is:

      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 is when :

            So, the result is:

          Now substitute back in:

        So, the result is:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            5   
 |                                 3      8*cos (x)
 | cos(3*x)*sin(2*x) dx = C + 2*cos (x) - ---------
 |                                            5    
/                                                  
$$\int \sin{\left(2 x \right)} \cos{\left(3 x \right)}\, dx = C - \frac{8 \cos^{5}{\left(x \right)}}{5} + 2 \cos^{3}{\left(x \right)}$$
The graph
The answer [src]
-2/5
$$- \frac{2}{5}$$
=
=
-2/5
$$- \frac{2}{5}$$
-2/5
Numerical answer [src]
-0.4
-0.4

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