What is the integral of (xcos(x))/2 ?

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

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integral of (xcos(x))/2

\int \frac{x cos ( x )}{2} d x

\frac{1}{2} (x sin (x) + cos (x)) + C

Solution steps

\int \frac{x cos ( x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

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

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

= \frac{1}{2} (x sin (x) - (- cos (x)))

Simplify

= \frac{1}{2} (x sin (x) + cos (x))

Add a constant to the solution

= \frac{1}{2} (x sin (x) + cos (x)) + C

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

\int \frac{2}{x ^{2} ( x ^{2} - 4 x - 5 )} d x

\int x^{3} sin^{2} (4 x) d x

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

\int \frac{x}{( a + x ) ^{2}} d x

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