What is the integral of (4400q)/(4q^2+320) ?

The integral of (4400q)/(4q^2+320) is 550ln|4q^2+320|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4400q)/(4q^2+320)

\int \frac{4400 q}{4 q ^{2} + 320} d q

550 ln 4 q^{2} + 320 + C

Solution steps

\int \frac{4400 q}{4 q ^{2} + 320} d q

Take the constant out:

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

= 4400 \cdot \int \frac{q}{4 q ^{2} + 320} d q

Apply u-substitution

: \int \frac{1}{8 u} d u

= 4400 \cdot \int \frac{1}{8 u} d u

Take the constant out:

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

= 4400 \cdot \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4400 \cdot \frac{1}{8} ln ∣ u ∣

Substitute back

u = 4 q^{2} + 320

= 4400 \cdot \frac{1}{8} ln 4 q^{2} + 320

Simplify

4400 \cdot \frac{1}{8} ln 4 q^{2} + 320 : 550 ln 4 q^{2} + 320

= 550 ln 4 q^{2} + 320

Add a constant to the solution

= 550 ln 4 q^{2} + 320 + C

y^{^{'}} = - 0.5 y^{1.5}

\frac{\partial}{\partial y} (x arcsin (\frac{y}{x}))

f (x) = (x + 5) (9 x + 5)

\frac{d}{d x} ((cos (x) + 2)^{3} (2 x)^{(- 3 x)})

\int (e^{- x^{2}}) d x

What is the integral of (4400q)/(4q^2+320) ?
The integral of (4400q)/(4q^2+320) is 550ln|4q^2+320|+C