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

\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

\frac{d}{d x} ((5 x^{2} + e)^{6})

n = 3 \sum \infty x^{n}

\frac{d}{d x} (\frac{6}{x} + \frac{x}{6})

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