What is the integral of-3/2 x*sin(x) ?

The integral of-3/2 x*sin(x) is -3/2 (-xcos(x)+sin(x))+C

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integral of-3/2 x*sin(x)

\int - \frac{3}{2} x \cdot sin (x) d x

- \frac{3}{2} (- x cos (x) + sin (x)) + C

Solution steps

\int - \frac{3}{2} x sin (x) d x

Take the constant out:

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

= - \frac{3}{2} \cdot \int x sin (x) d x

Apply Integration By Parts

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

= - \frac{3}{2} (- x cos (x) - \int - cos (x) d x)

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

= - \frac{3}{2} (- x cos (x) - (- sin (x)))

Simplify

= - \frac{3}{2} (- x cos (x) + sin (x))

Add a constant to the solution

= - \frac{3}{2} (- x cos (x) + sin (x)) + C

\frac{d}{d x} (5 - 3 x^{2})

- \frac{14}{( 2 + 15 ) ^{2}}

\int \frac{e ^{a r c t a n (x)}}{1 + x ^{2}} d x

(\frac{3 y ^{2} - t ^{2}}{y ^{5}}) \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

\frac{\partial}{\partial x} (x e^{- y})

What is the integral of-3/2 x*sin(x) ?
The integral of-3/2 x*sin(x) is -3/2 (-xcos(x)+sin(x))+C