What is the integral of 1/((1+x)) ?

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

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integral of 1/((1+x))

integral

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

ln ∣ 1 + x ∣ + C

Solution steps

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

= ln ∣ 1 + x ∣

Add a constant to the solution

= ln ∣ 1 + x ∣ + C

1 - cos^{2} (x)

(e^{x})^{3}

\frac{1}{( x ^{3} - 1 )}

x^{2} e^{x}

\frac{x}{( x ^{2} + 1 )}