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Popular >

integral of ln(2x^2+1)

Solution

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

Solution

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

Solution steps

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

Apply Integration By Parts

: x ln (2 x^{2} + 1) - \int \frac{4 x ^{2}}{2 x ^{2} + 1} d x

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

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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