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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

(1 + x^{2}) 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

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

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

\int 3 x^{4} - 3 x d x

\int sin (3 - x) d x

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

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