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

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

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integral of 2x*sin(x)

\int 2 x \cdot sin (x) d x

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

Solution steps

\int 2 x sin (x) d x

Take the constant out:

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

= 2 \cdot \int x sin (x) d x

Apply Integration By Parts

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

= 2 (- x cos (x) - \int - cos (x) d x)

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

= 2 (- x cos (x) - (- sin (x)))

Simplify

= 2 (- x cos (x) + sin (x))

Add a constant to the solution

= 2 (- x cos (x) + sin (x)) + C

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

x, 6 - x, [4, 9]

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

x \to - 6 lim (\frac{x ^{2} - 7}{6 - x})

\int_{0}^{0.5} 12 x - \frac{1}{12} x d x

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