What is the integral of ((t+2))/(tsqrt(t+1)) ?

The integral of ((t+2))/(tsqrt(t+1)) is 2sqrt(t+1)-4(1/2 ln|sqrt(t+1)+1|-1/2 ln|sqrt(t+1)-1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((t+2))/(tsqrt(t+1))

\int \frac{( t + 2 )}{t t + 1} d t

2 t + 1 - 4 (\frac{1}{2} ln t + 1 + 1 - \frac{1}{2} ln t + 1 - 1) + C

Solution steps

\int \frac{t + 2}{t t + 1} d t

Expand

\frac{t + 2}{t t + 1} : \frac{1}{t + 1} + \frac{2}{t t + 1}

= \int \frac{1}{t + 1} + \frac{2}{t t + 1} d t

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{1}{t + 1} d t + \int \frac{2}{t t + 1} d t

\int \frac{1}{t + 1} d t = 2 t + 1

\int \frac{2}{t t + 1} d t = - 4 (\frac{1}{2} ln t + 1 + 1 - \frac{1}{2} ln t + 1 - 1)

= 2 t + 1 - 4 (\frac{1}{2} ln t + 1 + 1 - \frac{1}{2} ln t + 1 - 1)

Add a constant to the solution

= 2 t + 1 - 4 (\frac{1}{2} ln t + 1 + 1 - \frac{1}{2} ln t + 1 - 1) + C

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

\int \frac{6}{x ^{2} - 7 x + 10} d x

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

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

\int \frac{6 x}{e ^{x}} d x

What is the integral of ((t+2))/(tsqrt(t+1)) ?
The integral of ((t+2))/(tsqrt(t+1)) is 2sqrt(t+1)-4(1/2 ln|sqrt(t+1)+1|-1/2 ln|sqrt(t+1)-1|)+C