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

The integral of x*sin(ax) is -1/a xcos(ax)+1/(a^2)sin(ax)+C

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integral of x*sin(ax)

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

- \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x) + C

Solution steps

\int x sin (a x) d x

Apply Integration By Parts

: - \frac{1}{a} x cos (a x) - \int - \frac{1}{a} cos (a x) d x

= - \frac{1}{a} x cos (a x) - \int - \frac{1}{a} cos (a x) d x

\int - \frac{1}{a} cos (a x) d x = - \frac{1}{a ^{2}} sin (a x)

= - \frac{1}{a} x cos (a x) - (- \frac{1}{a ^{2}} sin (a x))

Simplify

= - \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x)

Add a constant to the solution

= - \frac{1}{a} x cos (a x) + \frac{1}{a ^{2}} sin (a x) + C

n = 0 \sum \infty \frac{2 ^{n}}{100}

x^{2} y^{^{''}} + x y^{^{'}} - y = \frac{1}{x + 1}

x \to 1 - lim (\frac{x}{ln ( x )})

\int sin (x^{3} + 1) d x

\int \frac{( x + 3 )}{2 x ^{3} - 8 x} d x

What is the integral of x*sin(ax) ?
The integral of x*sin(ax) is -1/a xcos(ax)+1/(a^2)sin(ax)+C