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Popular Calculus >

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

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

Graph

Popular Examples

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

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

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

integral of (x^3+y^3)

\int (x^{3} + y^{3}) d x

integral of cos^3(3x)*sin^7(3x)

\int cos^{3} (3 x) \cdot sin^{7} (3 x) d x

Frequently Asked Questions (FAQ)

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