Mister Exam

Integral of xsin(x+2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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 |  x*sin(x + 2) dx
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$$\int\limits_{0}^{1} x \sin{\left(x + 2 \right)}\, dx$$
Integral(x*sin(x + 2), (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. Let .

      Then let and substitute :

      1. The integral of sine is negative cosine:

      Now substitute back in:

    Now evaluate the sub-integral.

  2. 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 cosine is sine:

      Now substitute back in:

    So, the result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                               
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 | x*sin(x + 2) dx = C - x*cos(2 + x) + sin(2 + x)
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$$\int x \sin{\left(x + 2 \right)}\, dx = C - x \cos{\left(x + 2 \right)} + \sin{\left(x + 2 \right)}$$
The graph
The answer [src]
-cos(3) - sin(2) + sin(3)
$$- \sin{\left(2 \right)} + \sin{\left(3 \right)} - \cos{\left(3 \right)}$$
=
=
-cos(3) - sin(2) + sin(3)
$$- \sin{\left(2 \right)} + \sin{\left(3 \right)} - \cos{\left(3 \right)}$$
-cos(3) - sin(2) + sin(3)
Numerical answer [src]
0.221815077834631
0.221815077834631
The graph
Integral of xsin(x+2) dx

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