What is the integral of ((1-x))/(sqrt(x^2+4x+3)) ?

The integral of ((1-x))/(sqrt(x^2+4x+3)) is 3ln|x+sqrt(x^2+4x+3)+2|-sqrt(x^2+4x+3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((1-x))/(sqrt(x^2+4x+3))

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

3 ln x + x^{2} + 4 x + 3 + 2 - x^{2} + 4 x + 3 + C

Solution steps

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

Expand

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

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

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

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

= ln x^{2} + 4 x + 3 + x + 2 - (x^{2} + 4 x + 3 - 2 ln x^{2} + 4 x + 3 + x + 2)

Simplify

= 3 ln x + x^{2} + 4 x + 3 + 2 - x^{2} + 4 x + 3

Add a constant to the solution

= 3 ln x + x^{2} + 4 x + 3 + 2 - x^{2} + 4 x + 3 + C

\int x 3 x^{2} - 4 d x

\int \frac{5 x}{( 3 - x ^{2} ) ^{3}} d x

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

\int \frac{e ^{r}}{r} d r

What is the integral of ((1-x))/(sqrt(x^2+4x+3)) ?
The integral of ((1-x))/(sqrt(x^2+4x+3)) is 3ln|x+sqrt(x^2+4x+3)+2|-sqrt(x^2+4x+3)+C