What is the integral of x^2cos(x+1) ?

The integral of x^2cos(x+1) is x^2sin(x+1)-2(-xcos(x+1)+sin(x+1))+C

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integral of x^2cos(x+1)

\int x^{2} cos (x + 1) d x

x^{2} sin (x + 1) - 2 (- x cos (x + 1) + sin (x + 1)) + C

Solution steps

\int x^{2} cos (x + 1) d x

Apply Integration By Parts

: x^{2} sin (x + 1) - \int 2 x sin (x + 1) d x

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

\int 2 x sin (x + 1) d x = 2 (- x cos (x + 1) + sin (x + 1))

= x^{2} sin (x + 1) - 2 (- x cos (x + 1) + sin (x + 1))

Add a constant to the solution

= x^{2} sin (x + 1) - 2 (- x cos (x + 1) + sin (x + 1)) + C

\frac{\partial}{\partial y} (- y sin (x y))

\int cos (2 a x) d x

8 y^{^{''}} - 7 y^{^{'}} + 3 y = 0

\int 5 x e^{- x^{2}} d x

f (x) = \frac{a x + b}{c x + d}

What is the integral of x^2cos(x+1) ?
The integral of x^2cos(x+1) is x^2sin(x+1)-2(-xcos(x+1)+sin(x+1))+C