What is the integral of xcos(n)x ?

The integral of xcos(n)x is 1/3 x^3cos(n)+C

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integral of xcos(n)x

\int x cos (n) x d x

\frac{1}{3} x^{3} cos (n) + C

Solution steps

\int x cos (n) x d x

Take the constant out:

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

= cos (n) \cdot \int xx d x

Simplify

xx : x^{2}

= cos (n) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= cos (n) \frac{x ^{3}}{3}

Simplify

cos (n) \frac{x ^{3}}{3} : \frac{1}{3} x^{3} cos (n)

= \frac{1}{3} x^{3} cos (n)

Add a constant to the solution

= \frac{1}{3} x^{3} cos (n) + C

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

y + 2 y^{7} = (y^{3} + 6 x) y^{^{'}}

x^{2} - x

x \to 0 + lim (\frac{x}{x + 1})

\frac{\partial}{\partial x} ((x + 2 y + 3 z)^{\frac{3}{2}})