What is the integral of 3xsin(x) ?

The integral of 3xsin(x) is 3(-xcos(x)+sin(x))+C

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integral of 3xsin(x)

\int 3 x sin (x) d x

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

Solution steps

\int 3 x sin (x) d x

Take the constant out:

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

= 3 \cdot \int x sin (x) d x

Apply Integration By Parts

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

= 3 (- x cos (x) - \int - cos (x) d x)

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

= 3 (- x cos (x) - (- sin (x)))

Simplify

= 3 (- x cos (x) + sin (x))

Add a constant to the solution

= 3 (- x cos (x) + sin (x)) + C

x \to 0 lim (x^{6} cos (\frac{8}{x}))

f (x) = \frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

\int_{0}^{2} \frac{x ^{2}}{x + 1} d x

\frac{d}{d x} (4 tan (x^{2} + x + 3))

y = \frac{x ^{3}}{6} + \frac{1}{2 x}

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