What is the integral of (sin(x+y)) ?

The integral of (sin(x+y)) is -cos(y+x)+C

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integral of (sin(x+y))

\int (sin (x + y)) d x

- cos (y + x) + C

Solution steps

\int sin (x + y) d x

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = y + x

= - cos (y + x)

Add a constant to the solution

= - cos (y + x) + C

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\frac{5}{x}

\frac{d}{d x} (3 x^{3} (x - 2))

\int_{0}^{1} x^{7} x^{4} + 1 d x

\frac{d y}{d x} = \frac{e ^{x} - 1}{e ^{y}}