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Solving integrals/ (cos(x)-xsin(x))y

Integral of (cos(x)-xsin(x))y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x                         
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 |  (cos(x) - x*sin(x))*y dx
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x0
$$\int\limits_{x_{0}}^{x} y \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$ 
Integral((cos(x) - x*sin(x))*y, (x, x0, x))
Detail solution

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

    1. Integrate term-by-term:

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

        1. Use integration by parts:

          Let and let .

          Then .

          To find :

          1. The integral of sine is negative cosine:

          Now evaluate the sub-integral.

        2. 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:

        So, the result is:

      1. The integral of cosine is sine:

      The result is:

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
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 | (cos(x) - x*sin(x))*y dx = C + x*y*cos(x)
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$$\int y \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx = C + x y \cos{\left(x \right)}$$
Simplify
The answer [src] 
x*y*cos(x) - x0*y*cos(x0)
$$x y \cos{\left(x \right)} - x_{0} y \cos{\left(x_{0} \right)}$$ 
=
= 
x*y*cos(x) - x0*y*cos(x0)
$$x y \cos{\left(x \right)} - x_{0} y \cos{\left(x_{0} \right)}$$ 
x*y*cos(x) - x0*y*cos(x0)

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

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