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) \cdot 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{sin ( x ) tan ( x )}{9 + sec ^{2} ( x )} d x

t^{2} y^{^{''}} + 21 t y^{^{'}} + 100 y = 0

f (x) = sin (x) + \frac{6}{7} cot (x)

x \to 2 lim (5 a + a x)

\frac{d y}{d x} - 5 y = e^{x}

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