What is the integral of-x*cos(x) ?

The integral of-x*cos(x) is -xsin(x)-cos(x)+C

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integral of-x*cos(x)

\int - x \cdot cos (x) d x

- x sin (x) - cos (x) + C

Solution steps

\int - x cos (x) d x

Take the constant out:

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

= - \int x cos (x) d x

Apply Integration By Parts

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

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

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

= - (x sin (x) - (- cos (x)))

Simplify

= - x sin (x) - cos (x)

Add a constant to the solution

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

\int \frac{8 x - 1}{( x - 2 ) ( x + 3 )} d x

\int x^{4} - x^{2} d x

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

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

\int \frac{x + 5}{x ^{2} - 6 x + 34} d x

What is the integral of-x*cos(x) ?
The integral of-x*cos(x) is -xsin(x)-cos(x)+C