What is the integral of ln(2x^2+5) ?

The integral of ln(2x^2+5) is xln(2x^2+5)-4(1/2 x-(sqrt(5))/(2sqrt(2))arctan(sqrt(2/5)x))+C

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integral of ln(2x^2+5)

\int ln (2 x^{2} + 5) d x

x ln (2 x^{2} + 5) - 4 (\frac{1}{2} x - \frac{5}{2 2} arctan (\frac{2}{5} x)) + C

Solution steps

\int ln (2 x^{2} + 5) d x

Apply Integration By Parts

: x ln (2 x^{2} + 5) - \int \frac{4 x ^{2}}{2 x ^{2} + 5} d x

= x ln (2 x^{2} + 5) - \int \frac{4 x ^{2}}{2 x ^{2} + 5} d x

\int \frac{4 x ^{2}}{2 x ^{2} + 5} d x = 4 (\frac{1}{2} x - \frac{5}{2 2} arctan (\frac{2}{5} x))

= x ln (2 x^{2} + 5) - 4 (\frac{1}{2} x - \frac{5}{2 2} arctan (\frac{2}{5} x))

Add a constant to the solution

= x ln (2 x^{2} + 5) - 4 (\frac{1}{2} x - \frac{5}{2 2} arctan (\frac{2}{5} x)) + C

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What is the integral of ln(2x^2+5) ?
The integral of ln(2x^2+5) is xln(2x^2+5)-4(1/2 x-(sqrt(5))/(2sqrt(2))arctan(sqrt(2/5)x))+C