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Popular >

integral of ln(x^2)+1

Solution

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

Solution

2 x ln (x) - x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 1 d x = x

= 2 x ln (x) - 2 x + x

Simplify

= 2 x ln (x) - x

Add a constant to the solution

= 2 x ln (x) - x + C

Popular Examples

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\int (\frac{1}{x - 5}) d x

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\int 2 sec^{6} (10 x) d x

integral of bsqrt(1-(x^2)/(a^2))

\int b 1 - \frac{x ^{2}}{a ^{2}} d x

Frequently Asked Questions (FAQ)

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