What is the integral of (1-x)cos(2x) ?

The integral of (1-x)cos(2x) is 1/2 sin(2x)-1/4 (2xsin(2x)+cos(2x))+C

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integral of (1-x)cos(2x)

\int (1 - x) cos (2 x) d x

\frac{1}{2} sin (2 x) - \frac{1}{4} (2 x sin (2 x) + cos (2 x)) + C

Solution steps

\int (1 - x) cos (2 x) d x

Expand

(1 - x) cos (2 x) : cos (2 x) - x cos (2 x)

= \int cos (2 x) - x cos (2 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 (2 x) d x - \int x cos (2 x) d x

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

\int x cos (2 x) d x = \frac{1}{4} (2 x sin (2 x) + cos (2 x))

= \frac{1}{2} sin (2 x) - \frac{1}{4} (2 x sin (2 x) + cos (2 x))

Add a constant to the solution

= \frac{1}{2} sin (2 x) - \frac{1}{4} (2 x sin (2 x) + cos (2 x)) + C

\frac{\partial}{\partial x} (e^{x} x + e^{x} 2 y)

\int \frac{sin ( nπ x )}{nπ} d x

\frac{d y}{d x} = \frac{1}{x ^{2} + 1}

\frac{d}{d x} (- 2 x^{\frac{9}{8}})

x \to 30 lim (30)

What is the integral of (1-x)cos(2x) ?
The integral of (1-x)cos(2x) is 1/2 sin(2x)-1/4 (2xsin(2x)+cos(2x))+C