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

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

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integral of cos(x)-xsin(x)

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

x cos (x) + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Simplify

= x cos (x)

Add a constant to the solution

= x cos (x) + C

e^{- x^{62}}

y^{^{'}} = x - 2 y

(1, 4), (- 5, 2)

\int \frac{1}{12 x - 9 x ^{2} - 2} d x

3 x y

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