What is the integral from 0 to x of xcos(x) ?

The integral from 0 to x of xcos(x) is xsin(x)+cos(x)-1

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integral from 0 to x of xcos(x)

\int_{0}^{x} x cos (x) d x

x sin (x) + cos (x) - 1

Solution steps

\int_{0}^{x} x cos (x) d x

Apply Integration By Parts

: [x sin (x) - \int sin (x) d x]_{0}^{x}

= [x sin (x) - \int sin (x) d x]_{0}^{x}

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

= [x sin (x) - (- cos (x))]_{0}^{x}

Simplify

= [x sin (x) + cos (x)]_{0}^{x}

Compute the boundaries:

x sin (x) + cos (x) - 1

= x sin (x) + cos (x) - 1

\int_{0}^{1} x 56 x^{2} + 25 d x

\int_{- \frac{5 π}{6}}^{0} sin (x) d x

\int_{- 3}^{3} (y + 2 ∣ y ∣) d y

\int_{b}^{\infty} \frac{1}{x} d x

\int_{0}^{\frac{1}{2}} arcsin (y) d y

What is the integral from 0 to x of xcos(x) ?
The integral from 0 to x of xcos(x) is xsin(x)+cos(x)-1