What is the integral of (esqrt(x+1))/(sqrt(x)) ?

The integral of (esqrt(x+1))/(sqrt(x)) is e(sqrt((x+1)/x)x+ln|sqrt(x+1)+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 (esqrt(x+1))/(sqrt(x))

\int \frac{e x + 1}{x} d x

e (\frac{x + 1}{x} x + ln x + 1 + x) + C

Solution steps

\int \frac{e x + 1}{x} d x

Take the constant out:

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

= e \cdot \int \frac{x + 1}{x} d x

Apply Integration By Parts

: \frac{x + 1}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}} x + 1} d x

= e (\frac{x + 1}{x} x - \int - \frac{1}{2 x ^{\frac{1}{2}} x + 1} d x)

\int - \frac{1}{2 x ^{\frac{1}{2}} x + 1} d x = - ln x + 1 + x

= e (\frac{x + 1}{x} x - (- ln x + 1 + x))

Simplify

= e (\frac{x + 1}{x} x + ln x + 1 + x)

Add a constant to the solution

= e (\frac{x + 1}{x} x + ln x + 1 + x) + C

\int \frac{3}{x ^{2}} + 4 - \frac{1}{4 x ^{3}} d x

\int x (7 x^{2} - 9)^{\frac{5}{2}} d x

\int x^{2} ln (x^{3} + 1) d x

\int 6 csc (x) cot (x) - sec (x) tan (x) d x

\int \frac{5}{x ^{2} - 4 x + 9} d x

What is the integral of (esqrt(x+1))/(sqrt(x)) ?
The integral of (esqrt(x+1))/(sqrt(x)) is e(sqrt((x+1)/x)x+ln|sqrt(x+1)+sqrt(x)|)+C