What is the integral of (ln(x))/((1+x^2)^{1.5)} ?

The integral of (ln(x))/((1+x^2)^{1.5)} is (xln(x))/(sqrt(1+x^2))-ln|sqrt(x^2+1)+x|+C

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integral of (ln(x))/((1+x^2)^{1.5)}

\int \frac{ln ( x )}{( 1 + x ^{2} ) ^{1.5}} d x

\frac{x ln ( x )}{1 + x ^{2}} - ln x^{2} + 1 + x + C

Solution steps

\int \frac{ln ( x )}{( 1 + x ^{2} ) ^{1.5}} d x

Apply Integration By Parts

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

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

\int \frac{1}{1 + x ^{2}} d x = ln x^{2} + 1 + x

= \frac{x ln ( x )}{1 + x ^{2}} - ln x^{2} + 1 + x

Add a constant to the solution

= \frac{x ln ( x )}{1 + x ^{2}} - ln x^{2} + 1 + x + C

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What is the integral of (ln(x))/((1+x^2)^{1.5)} ?
The integral of (ln(x))/((1+x^2)^{1.5)} is (xln(x))/(sqrt(1+x^2))-ln|sqrt(x^2+1)+x|+C