What is the integral of-xcos(x) ?

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

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integral of-xcos(x)

\int - x 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

\frac{\partial}{\partial x} (A e^{- 3 x})

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 1, y^{^{'}} (0) = - 5

f (x) = arccos (e^{2 x})

x^{3} - 8 x^{2} + 12 x, - x^{3} + 8 x^{2} - 12 x

y = \frac{7}{( 1 - x ^{2} ) ^{3}}