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

The integral of x^2-ln(x^2)+k is (x^3)/3-2xln(x)+2x+kx+C

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integral of x^2-ln(x^2)+k

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

\frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x + C

Solution steps

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

\int k d x = k x

= \frac{x ^{3}}{3} - (2 x ln (x) - 2 x) + k x

Simplify

= \frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 x ln (x) + 2 x + k x + C

\int_{1}^{5} 1 d x

\int x^{2} \cdot e^{- a x} d x

\frac{1}{( x - 1 )}

x \to 2 lim (ln (\frac{x}{x ^{2} - 4}))

a y (e^{b y})

What is the integral of x^2-ln(x^2)+k ?
The integral of x^2-ln(x^2)+k is (x^3)/3-2xln(x)+2x+kx+C