What is the integral of 13xsin(x) ?

The integral of 13xsin(x) is 13(-xcos(x)+sin(x))+C

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integral of 13xsin(x)

\int 13 x sin (x) d x

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

Solution steps

\int 13 x sin (x) d x

Take the constant out:

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

= 13 \cdot \int x sin (x) d x

Apply Integration By Parts

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

= 13 (- x cos (x) - \int - cos (x) d x)

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

= 13 (- x cos (x) - (- sin (x)))

Simplify

= 13 (- x cos (x) + sin (x))

Add a constant to the solution

= 13 (- x cos (x) + sin (x)) + C

y^{^{'}} = y (x y^{2} + 5)

\int 3 (x) cos (\frac{x}{3}) d x

\frac{d}{d x} ((x - 1) \cdot x^{2} - 2 x + 2)

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

\frac{d}{d y} (y^{\frac{2}{3}})

What is the integral of 13xsin(x) ?
The integral of 13xsin(x) is 13(-xcos(x)+sin(x))+C