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

The integral of x(cos(x)+1) is xsin(x)+x^2+cos(x)-(x^2)/2+C

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integral of x(cos(x)+1)

\int x (cos (x) + 1) d x

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

Solution steps

\int x (cos (x) + 1) d x

Apply Integration By Parts

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

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

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

Simplify

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

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

Add a constant to the solution

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

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