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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Simplify

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

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

Add a constant to the solution

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

d er i v a t i v e f (x) = 4 lo g_{6} (2)

t an g e n t f (x) = \frac{1}{2 x}, at x = 65

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

d er i v a t i v e f (x) = \frac{e ^{x}}{x ^{6}}

\int 4 t^{3} t^{2} + 1 d t

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