What is the integral of xcos(pi)x ?

The integral of xcos(pi)x is -(x^3)/3+C

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integral of xcos(pi)x

\int x cos (π) x d x

- \frac{x ^{3}}{3} + C

Solution steps

\int x cos (π) x d x

Take the constant out:

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

= cos (π) \cdot \int xx d x

cos (π) = - 1

= (- 1) \cdot \int xx d x

Simplify

xx : x^{2}

= (- 1) \cdot \int x^{2} d x

Apply the Power Rule

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

= (- 1) \frac{x ^{3}}{3}

Simplify

= - \frac{x ^{3}}{3}

Add a constant to the solution

= - \frac{x ^{3}}{3} + C

y = x, y = 0, x = 4

\frac{d y}{d x} = x^{2} y^{2} + x^{2} + y^{2} + 1

\int_{0}^{1} (e^{\frac{2 x}{3}} + 1) d x

y^{^{''}} + (2 \cdot 0.1096) y^{^{'}} + (4.51 5^{2}) y = 0

(t^{2} + 9) y^{^{'}} + 2 t y = t^{2} (t^{2} + 9)