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

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

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integral of x(sin(x))

\int x (sin (x)) d x

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

Solution steps

\int x sin (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

x \to 0 lim (\frac{x}{∣ x ∣ + x})

n = 1 \sum \infty \frac{1}{10 n + 1}

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{3} + 1})

\int \frac{3 ( 2 + ln ( - 3 x ) ) ^{3}}{x} d x

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