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

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

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integral of (x^2+1)cos(x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

x \to 2 lim (x^{2} - \frac{4}{x - 2})

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

\frac{d y}{d x} = (\frac{y}{x})

\frac{d}{d x} (x^{4} sin (x) sin (3 x))

\frac{d}{d x} (3 (1 - x)^{- 2})

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