en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of v/(v^2+1)

Solution

\int \frac{v}{v ^{2} + 1} d v

Solution

\frac{1}{2} ln v^{2} + 1 + C

Solution steps

\int \frac{v}{v ^{2} + 1} d v

Apply u-substitution

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

= \int \frac{1}{2 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = v^{2} + 1

= \frac{1}{2} ln v^{2} + 1

Add a constant to the solution

= \frac{1}{2} ln v^{2} + 1 + C

Popular Examples

integral of (x^2+6)/(x^3+x^2-2x)

\int \frac{x ^{2} + 6}{x ^{3} + x ^{2} - 2 x} d x

tangent of f(x)= 2/(x+7),(-8,-2)tangent of

f (x) = \frac{2}{x + 7}, (- 8, - 2)

derivative of e^xarctan(x)

\frac{d}{d x} (e^{x} arctan (x))

x((dy)/(dx))= 1/(y^3)

x (\frac{d y}{d x}) = \frac{1}{y ^{3}}

(dy)/(dx)=(x+y+4)^2

\frac{d y}{d x} = (x + y + 4)^{2}

Frequently Asked Questions (FAQ)

What is the integral of v/(v^2+1) ?
The integral of v/(v^2+1) is 1/2 ln|v^2+1|+C