Integral of cos(x+y) dx

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$$\int\limits_{0}^{1} \cos{\left(x + y \right)}\, dx$$

Integral(cos(x + y), (x, 0, 1))

Detail solution

Let $u = x + y$ .

Then let $du = dx$ and substitute $du$ :

$\int \cos{\left(u \right)}\, du$
1. The integral of cosine is sine:
  
  $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
Now substitute $u$ back in:

$\sin{\left(x + y \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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 | cos(x + y) dx = C + sin(x + y)
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$$\int \cos{\left(x + y \right)}\, dx = C + \sin{\left(x + y \right)}$$

Simplify

The answer [src]

-sin(y) + sin(1 + y)

$$- \sin{\left(y \right)} + \sin{\left(y + 1 \right)}$$

-sin(y) + sin(1 + y)

$$- \sin{\left(y \right)} + \sin{\left(y + 1 \right)}$$

-sin(y) + sin(1 + y)

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