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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{5 x + 1}{9 x ^{2} + 6 x + 3} d x

\int x^{3} cos (7 x) d x

\int \frac{1 - x ^{2}}{1 - x ^{2}} d x

\int x (x^{2} + 5)^{7} d x

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