What is the integral of (2+sin(x))/(sqrt(x)) ?

The integral of (2+sin(x))/(sqrt(x)) is 2(2sqrt(x)+sqrt(pi/2)\S(sqrt(2/pi)sqrt(x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2+sin(x))/(sqrt(x))

\int \frac{2 + sin ( x )}{x} d x

2 (2 x + \frac{π}{2} § (\frac{2}{π} x)) + C

Solution steps

\int \frac{2 + sin ( x )}{x} d x

Apply u-substitution

: \int 2 (2 + sin (u^{2})) d u

= \int 2 (2 + sin (u^{2})) d u

Take the constant out:

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

= 2 \cdot \int 2 + sin (u^{2}) d u

Apply the Sum Rule:

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

= 2 (\int 2 d u + \int sin (u^{2}) d u)

\int 2 d u = 2 u

\int sin (u^{2}) d u = \frac{π}{2} § (\frac{2}{π} u)

= 2 (2 u + \frac{π}{2} § (\frac{2}{π} u))

Substitute back

u = x

= 2 (2 x + \frac{π}{2} § (\frac{2}{π} x))

Add a constant to the solution

= 2 (2 x + \frac{π}{2} § (\frac{2}{π} x)) + C

\int e^{\frac{- x}{100}} d x

\int sec^{2} (1 - 2 x) tan^{2} (1 - 2 x) d x

\int sin (ln (x^{3})) d x

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

\int (x + 4) (3 x - 5) d x

What is the integral of (2+sin(x))/(sqrt(x)) ?
The integral of (2+sin(x))/(sqrt(x)) is 2(2sqrt(x)+sqrt(pi/2)\S(sqrt(2/pi)sqrt(x)))+C