What is the integral of sin(x)*x ?

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

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integral of sin(x)*x

\int sin (x) \cdot x d x

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

Solution steps

\int sin (x) x d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

- \frac{6}{x ^{3}}

\int x arctan (x) d x

\frac{\partial}{\partial x} (x^{4} + 12 x y^{2} + 2 y^{4})

y = \frac{2 x - 9}{3 x + 7}

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