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Popular >

integral of 1/(x+1)

Solution

integral

\frac{1}{x + 1}

Solution

ln ∣ x + 1 ∣ + C

Solution steps

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

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 = x + 1

= ln ∣ x + 1 ∣

Add a constant to the solution

= ln ∣ x + 1 ∣ + C

Popular Examples

integral of (6e^x-x^3(sqrt(x)+1))

\int (6 e^{x} - x^{3} (x + 1)) d x

integral of (x^2+x+8)sqrt(x+7)

\int (x^{2} + x + 8) x + 7 d x

integral of (tanh^2(1/x))/(x^2)

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

integral of (a-x)^2

\int (a - x)^{2} d x

integral of (5t^2+7)/(t^{4/3)}

\int \frac{5 t ^{2} + 7}{t ^{\frac{4}{3}}} d t

Frequently Asked Questions (FAQ)

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