What is the integral of xsin(y) ?

The integral of xsin(y) is -xcos(y)+C

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integral of xsin(y)

\int x sin (y) d y

- x cos (y) + C

Solution steps

\int x sin (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int sin (y) d y

Use the common integral:

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

= x (- cos (y))

Simplify

= - x cos (y)

Add a constant to the solution

= - x cos (y) + C

\int \frac{- 2}{x ^{3} - x} d x

\int_{1}^{b} \frac{1}{( x + 4 ) ^{2}} d x

\int \frac{1}{6} sin (6 t) d t

f (x) = 3 + x^{2}

y = x^{2} - x + 2, at x = 2