What is the integral of 1/(3shx+5chx) ?

The integral of 1/(3shx+5chx) is 1/(3sh+5ch)ln|3shx+5chx|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(3shx+5chx)

\int \frac{1}{3 s h x + 5 c h x} d x

\frac{1}{3 s h + 5 c h} ln ∣ 3 s h x + 5 c h x ∣ + C

Solution steps

\int \frac{1}{3 s h x + 5 c h x} d x

Apply u-substitution

: \int \frac{1}{u ( 3 s h + 5 c h )} d u

= \int \frac{1}{u ( 3 s h + 5 c h )} d u

Take the constant out:

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

= \frac{1}{3 s h + 5 c h} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3 s h + 5 c h} ln ∣ u ∣

Substitute back

u = 3 s h x + 5 c h x

= \frac{1}{3 s h + 5 c h} ln ∣ 3 s h x + 5 c h x ∣

Add a constant to the solution

= \frac{1}{3 s h + 5 c h} ln ∣ 3 s h x + 5 c h x ∣ + C

\frac{5 s}{( s ^{2} + 4 ) ( s + 1 )}

\frac{d y}{d x} = 0.002 y (500 - y) - 80

\frac{d}{d x} (x - 16)

\int e^{- 0.1 t} d t

\int_{0}^{\infty} e^{2 x} d x

What is the integral of 1/(3shx+5chx) ?
The integral of 1/(3shx+5chx) is 1/(3sh+5ch)ln|3shx+5chx|+C