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Popular >

integral of 1/(r+1)

Solution

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

Solution

ln ∣ r + 1 ∣ + C

Solution steps

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

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 = r + 1

= ln ∣ r + 1 ∣

Add a constant to the solution

= ln ∣ r + 1 ∣ + C

Popular Examples

integral of e^{2x}cos(pi)x

\int e^{2 x} cos (π) x d x

integral of (50)/(x+5)

\int \frac{50}{x + 5} d x

integral of 1/((x+5))

\int \frac{1}{( x + 5 )} d x

integral of ln(x^2+2x)

\int ln (x^{2} + 2 x) d x

integral of (3x^2+19x+27)/((x+2)(x+3)^2)

\int \frac{3 x ^{2} + 19 x + 27}{( x + 2 ) ( x + 3 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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