What is the integral of (10)/(x^2+2x+10) ?

The integral of (10)/(x^2+2x+10) is 10/3 arctan(1/3 (x+1))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (10)/(x^2+2x+10)

\int \frac{10}{x ^{2} + 2 x + 10} d x

\frac{10}{3} arctan (\frac{1}{3} (x + 1)) + C

Solution steps

\int \frac{10}{x ^{2} + 2 x + 10} d x

Take the constant out:

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

= 10 \cdot \int \frac{1}{x ^{2} + 2 x + 10} d x

Complete the square

x^{2} + 2 x + 10 : (x + 1)^{2} + 9

= 10 \cdot \int \frac{1}{( x + 1 ) ^{2} + 9} d x

Apply u-substitution

: \int \frac{1}{u ^{2} + 9} d u

= 10 \cdot \int \frac{1}{u ^{2} + 9} d u

Apply Integral Substitution

= 10 \cdot \int \frac{1}{3 ( v ^{2} + 1 )} d v

Take the constant out:

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

= 10 \cdot \frac{1}{3} \cdot \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= 10 \cdot \frac{1}{3} arctan (v)

Substitute back

= 10 \cdot \frac{1}{3} arctan (\frac{x + 1}{3})

Simplify

10 \cdot \frac{1}{3} arctan (\frac{x + 1}{3}) : \frac{10}{3} arctan (\frac{1}{3} (x + 1))

= \frac{10}{3} arctan (\frac{1}{3} (x + 1))

Add a constant to the solution

= \frac{10}{3} arctan (\frac{1}{3} (x + 1)) + C

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

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

\int 20 + 0.2 x d x

\int 4 cosh (x) + x^{3} d x

\int \frac{1}{x ^{2} 11 - x ^{2}} d x

What is the integral of (10)/(x^2+2x+10) ?
The integral of (10)/(x^2+2x+10) is 10/3 arctan(1/3 (x+1))+C