What is the integral of (cosh(sqrt(x))+3)/(sqrt(x)) ?

The integral of (cosh(sqrt(x))+3)/(sqrt(x)) is 2sinh(sqrt(x))+6sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cosh(sqrt(x))+3)/(sqrt(x))

\int \frac{cosh ( x ) + 3}{x} d x

2 sinh (x) + 6 x + C

Solution steps

\int \frac{cosh ( x ) + 3}{x} d x

Expand

\frac{cosh ( x ) + 3}{x} : \frac{cosh ( x )}{x} + \frac{3}{x}

= \int \frac{cosh ( x )}{x} + \frac{3}{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 \frac{cosh ( x )}{x} d x + \int \frac{3}{x} d x

\int \frac{cosh ( x )}{x} d x = 2 sinh (x)

\int \frac{3}{x} d x = 6 x

= 2 sinh (x) + 6 x

Add a constant to the solution

= 2 sinh (x) + 6 x + C

\int \frac{20000}{x ^{2}} d x

\int \frac{x}{cos ^{2} ( 1 - 4 x ^{2} )} d x

\int 5 - 3 x d x

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

\int \frac{1}{sin ( x + \frac{π}{4} )} d x

What is the integral of (cosh(sqrt(x))+3)/(sqrt(x)) ?
The integral of (cosh(sqrt(x))+3)/(sqrt(x)) is 2sinh(sqrt(x))+6sqrt(x)+C