What is the integral of (7x)/((x^2+2)^2) ?

The integral of (7x)/((x^2+2)^2) is -7/(2(x^2+2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (7x)/((x^2+2)^2)

\int \frac{7 x}{( x ^{2} + 2 ) ^{2}} d x

- \frac{7}{2 ( x ^{2} + 2 )} + C

Solution steps

\int \frac{7 x}{( x ^{2} + 2 ) ^{2}} d x

Take the constant out:

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

= 7 \cdot \int \frac{x}{( x ^{2} + 2 ) ^{2}} d x

Apply u-substitution

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

= 7 \cdot \int \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= 7 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 7 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = x^{2} + 2

= 7 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 2})

Simplify

7 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 2}) : - \frac{7}{2 ( x ^{2} + 2 )}

= - \frac{7}{2 ( x ^{2} + 2 )}

Add a constant to the solution

= - \frac{7}{2 ( x ^{2} + 2 )} + C

\frac{\partial}{\partial y} (x y cos (z))

\int sin (x y) d x

\int_{- 1}^{x} 1.5 x^{2} d x

f (x) = \frac{x ^{5} + 4 x}{x ^{3}}

y^{^{'}} = (1 - y) \cdot sin (x)

What is the integral of (7x)/((x^2+2)^2) ?
The integral of (7x)/((x^2+2)^2) is -7/(2(x^2+2))+C