What is the integral of (x-5)sin(x) ?

The integral of (x-5)sin(x) is -cos(x)(x-5)+sin(x)+C

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integral of (x-5)sin(x)

\int (x - 5) sin (x) d x

- cos (x) (x - 5) + sin (x) + C

Solution steps

\int (x - 5) sin (x) d x

Apply Integration By Parts

: - cos (x) (x - 5) - \int - cos (x) d x

= - cos (x) (x - 5) - \int - cos (x) d x

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

= - cos (x) (x - 5) - (- sin (x))

Simplify

= - cos (x) (x - 5) + sin (x)

Add a constant to the solution

= - cos (x) (x - 5) + sin (x) + C

\int (\frac{( x + 1 )}{x}) d x

\int x^{8} + 2 x^{6} + x^{4} d x

3 t (\frac{d y}{d t}) + y = t^{2}

f (x) = x^{2} + 16

(2 x y + 2 x) d x - (1 + x^{4}) d y = 0

What is the integral of (x-5)sin(x) ?
The integral of (x-5)sin(x) is -cos(x)(x-5)+sin(x)+C