What is the integral of (r/3)cos(r/3) ?

The integral of (r/3)cos(r/3) is rsin(r/3)+3cos(r/3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (r/3)cos(r/3)

\int (\frac{r}{3}) cos (\frac{r}{3}) d r

r sin (\frac{r}{3}) + 3 cos (\frac{r}{3}) + C

Solution steps

\int \frac{r}{3} cos (\frac{r}{3}) d r

Take the constant out:

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

= \frac{1}{3} \cdot \int r cos (\frac{r}{3}) d r

Apply Integration By Parts

: 3 r sin (\frac{r}{3}) - \int 3 sin (\frac{r}{3}) d r

= \frac{1}{3} (3 r sin (\frac{r}{3}) - \int 3 sin (\frac{r}{3}) d r)

\int 3 sin (\frac{r}{3}) d r = - 9 cos (\frac{r}{3})

= \frac{1}{3} (3 r sin (\frac{r}{3}) - (- 9 cos (\frac{r}{3})))

Simplify

\frac{1}{3} (3 r sin (\frac{r}{3}) - (- 9 cos (\frac{r}{3}))) : r sin (\frac{r}{3}) + 3 cos (\frac{r}{3})

= r sin (\frac{r}{3}) + 3 cos (\frac{r}{3})

Add a constant to the solution

= r sin (\frac{r}{3}) + 3 cos (\frac{r}{3}) + C

\frac{6 ( s + 1 )}{s ^{2} ( s + 1 )}

\frac{\partial}{\partial x} (arcsin (2 x))

\int (x y) d x

y^{^{''}} + 81 y = 0, y (0) = 3, y^{^{'}} (0) = 5

x^{\frac{1}{2}}, x^{2}

What is the integral of (r/3)cos(r/3) ?
The integral of (r/3)cos(r/3) is rsin(r/3)+3cos(r/3)+C