What is the integral of (10800q)/(9q^2+675) ?

The integral of (10800q)/(9q^2+675) is 600ln|9q^2+675|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (10800q)/(9q^2+675)

\int \frac{10800 q}{9 q ^{2} + 675} d q

600 ln 9 q^{2} + 675 + C

Solution steps

\int \frac{10800 q}{9 q ^{2} + 675} d q

Take the constant out:

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

= 10800 \cdot \int \frac{q}{9 q ^{2} + 675} d q

Apply u-substitution

: \int \frac{1}{18 u} d u

= 10800 \cdot \int \frac{1}{18 u} d u

Take the constant out:

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

= 10800 \cdot \frac{1}{18} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 10800 \cdot \frac{1}{18} ln ∣ u ∣

Substitute back

u = 9 q^{2} + 675

= 10800 \cdot \frac{1}{18} ln 9 q^{2} + 675

Simplify

10800 \cdot \frac{1}{18} ln 9 q^{2} + 675 : 600 ln 9 q^{2} + 675

= 600 ln 9 q^{2} + 675

Add a constant to the solution

= 600 ln 9 q^{2} + 675 + C

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

f (x) = x^{3}, (0, 0)

f (x) = 3 (5 - x)^{2}

\frac{d}{d x} ((9 x + 2)^{\frac{2}{3}})

\int sin (a x) cos (a x) d x

What is the integral of (10800q)/(9q^2+675) ?
The integral of (10800q)/(9q^2+675) is 600ln|9q^2+675|+C