What is the integral of (x^2+8x)cos(x) ?

The integral of (x^2+8x)cos(x) is x^2sin(x)+8xsin(x)+2xcos(x)+8cos(x)-2sin(x)+C

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integral of (x^2+8x)cos(x)

\int (x^{2} + 8 x) cos (x) d x

x^{2} sin (x) + 8 x sin (x) + 2 x cos (x) + 8 cos (x) - 2 sin (x) + C

Solution steps

\int (x^{2} + 8 x) cos (x) d x

Apply Integration By Parts

: (x^{2} + 8 x) sin (x) - \int (2 x + 8) sin (x) d x

= (x^{2} + 8 x) sin (x) - \int (2 x + 8) sin (x) d x

\int (2 x + 8) sin (x) d x = - cos (x) (2 x + 8) + 2 sin (x)

= (x^{2} + 8 x) sin (x) - (- cos (x) (2 x + 8) + 2 sin (x))

Simplify

(x^{2} + 8 x) sin (x) - (- cos (x) (2 x + 8) + 2 sin (x)) : x^{2} sin (x) + 8 x sin (x) + 2 x cos (x) + 8 cos (x) - 2 sin (x)

= x^{2} sin (x) + 8 x sin (x) + 2 x cos (x) + 8 cos (x) - 2 sin (x)

Add a constant to the solution

= x^{2} sin (x) + 8 x sin (x) + 2 x cos (x) + 8 cos (x) - 2 sin (x) + C

\frac{d}{d x} ((2 x)^{\frac{1}{2}})

\frac{d}{d x} (cos (x^{2} e^{x}))

x \to - 2 lim (- x^{2} + 5 x - 1)

F (s) = \frac{s ^{2} - 2 s - 6}{s - 2}

x \to 3 + lim (\frac{x + 2}{x - 2})

What is the integral of (x^2+8x)cos(x) ?
The integral of (x^2+8x)cos(x) is x^2sin(x)+8xsin(x)+2xcos(x)+8cos(x)-2sin(x)+C