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Popular >

integral of 1/(1+v)

Solution

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

Solution

ln ∣ 1 + v ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + v

= ln ∣ 1 + v ∣

Add a constant to the solution

= ln ∣ 1 + v ∣ + C

Popular Examples

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

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

integral of e^{-2z}

\int e^{- 2 z} d z

integral of (sqrt(100-x^2))/(x^2)

\int \frac{100 - x ^{2}}{x ^{2}} d x

integral of (9-e^x)/(e^{5x)}

\int \frac{9 - e ^{x}}{e ^{5 x}} d x

integral of (1/(sqrt(y-2))+3y^2)

\int (\frac{1}{y - 2} + 3 y^{2}) d y

Frequently Asked Questions (FAQ)

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