Mister Exam

Integral of cos(x+y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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01cos(x+y)dx\int\limits_{0}^{1} \cos{\left(x + y \right)}\, dx
Integral(cos(x + y), (x, 0, 1))
Detail solution
  1. Let u=x+yu = x + y.

    Then let du=dxdu = dx and substitute dudu:

    cos(u)du\int \cos{\left(u \right)}\, du

    1. The integral of cosine is sine:

      cos(u)du=sin(u)\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}

    Now substitute uu back in:

    sin(x+y)\sin{\left(x + y \right)}

  2. Add the constant of integration:

    sin(x+y)+constant\sin{\left(x + y \right)}+ \mathrm{constant}


The answer is:

sin(x+y)+constant\sin{\left(x + y \right)}+ \mathrm{constant}

The answer (Indefinite) [src]
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cos(x+y)dx=C+sin(x+y)\int \cos{\left(x + y \right)}\, dx = C + \sin{\left(x + y \right)}
The answer [src]
-sin(y) + sin(1 + y)
sin(y)+sin(y+1)- \sin{\left(y \right)} + \sin{\left(y + 1 \right)}
=
=
-sin(y) + sin(1 + y)
sin(y)+sin(y+1)- \sin{\left(y \right)} + \sin{\left(y + 1 \right)}
-sin(y) + sin(1 + y)

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