What is the integral of (x-1)cos(x/3) ?

The integral of (x-1)cos(x/3) is 3xsin(x/3)+9cos(x/3)-3sin(x/3)+C

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integral of (x-1)cos(x/3)

\int (x - 1) cos (\frac{x}{3}) d x

3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3}) + C

Solution steps

\int (x - 1) cos (\frac{x}{3}) d x

Expand

(x - 1) cos (\frac{x}{3}) : x cos (\frac{x}{3}) - cos (\frac{x}{3})

= \int x cos (\frac{x}{3}) - cos (\frac{x}{3}) 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 x cos (\frac{x}{3}) d x - \int cos (\frac{x}{3}) d x

\int x cos (\frac{x}{3}) d x = 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3})

\int cos (\frac{x}{3}) d x = 3 sin (\frac{x}{3})

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3})

Add a constant to the solution

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3}) + C

\frac{d}{d x} (x^{0.2})

e^{6 s i n (7 x)}

\frac{d}{d x} (\frac{π}{3})

\int \frac{1}{7 + 8 x ^{2}} d x

n = 0 \sum \infty n! (x - 4)^{n}

What is the integral of (x-1)cos(x/3) ?
The integral of (x-1)cos(x/3) is 3xsin(x/3)+9cos(x/3)-3sin(x/3)+C