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Popular >

integral of (1/x+1)

Solution

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

Solution

ln ∣ x ∣ + x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 1 d x = x

= ln ∣ x ∣ + x

Add a constant to the solution

= ln ∣ x ∣ + x + C

Popular Examples

integral of x(5x^2-6)^4

\int x (5 x^{2} - 6)^{4} d x

integral of 2/(x(1+x))

\int \frac{2}{x ( 1 + x )} d x

integral of (x-18)/(4x^3+9x)

\int \frac{x - 18}{4 x ^{3} + 9 x} d x

integral of (x+1)/(sqrt(x^2+2x+5))

\int \frac{x + 1}{x ^{2} + 2 x + 5} d x

integral of 2x^2sqrt(4x^3-7)

\int 2 x^{2} 4 x^{3} - 7 d x

Frequently Asked Questions (FAQ)

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