What is the integral of (x^2+5x)cos(x) ?

The integral of (x^2+5x)cos(x) is x^2sin(x)+5xsin(x)+2xcos(x)+5cos(x)-2sin(x)+C

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integral of (x^2+5x)cos(x)

\int (x^{2} + 5 x) cos (x) d x

x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

Solution steps

\int (x^{2} + 5 x) cos (x) d x

Apply Integration By Parts

: (x^{2} + 5 x) sin (x) - \int (2 x + 5) sin (x) d x

= (x^{2} + 5 x) sin (x) - \int (2 x + 5) sin (x) d x

\int (2 x + 5) sin (x) d x = - cos (x) (2 x + 5) + 2 sin (x)

= (x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x))

Simplify

(x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x)) : x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

Add a constant to the solution

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

\frac{d y}{d x} = 0.5 y

\frac{d}{d x} (\frac{8 x ^{2} - 40}{3 x ^{\frac{1}{3}}})

x \to 0 + lim (\frac{∣ 2 x ∣}{x})

n \to \infty lim (A r g (- 1 + \frac{i}{n}))

x \to \infty + lim (\frac{11}{2})

What is the integral of (x^2+5x)cos(x) ?
The integral of (x^2+5x)cos(x) is x^2sin(x)+5xsin(x)+2xcos(x)+5cos(x)-2sin(x)+C