What is the integral of ((1+x^2))/(x(1+x^2)) ?

The integral of ((1+x^2))/(x(1+x^2)) is ln|x|+C

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

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

ln ∣ x ∣ + C

Solution steps

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

Cancel the common factor:

1 + x^{2}

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

\int (3 - ∣ x - 3 ∣) d x

\int \frac{1}{nπ} sin (nπ x) d x

\int (\frac{1}{t ^{2}}) d t

\int \frac{1}{y ^{3}} d y

\int \frac{1}{3} sin (3 t) d t

What is the integral of ((1+x^2))/(x(1+x^2)) ?
The integral of ((1+x^2))/(x(1+x^2)) is ln|x|+C