What is the integral of ((a^2-x^2))/x ?

The integral of ((a^2-x^2))/x is a^2ln|x|-(x^2)/2+C

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

integral

\frac{( a ^{2} - x ^{2} )}{x}

a^{2} ln ∣ x ∣ - \frac{x ^{2}}{2} + C

Solution steps

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

Expand

\frac{a ^{2} - x ^{2}}{x} : \frac{a ^{2}}{x} - x

= \int \frac{a ^{2}}{x} - x 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 \frac{a ^{2}}{x} d x - \int x d x

\int \frac{a ^{2}}{x} d x = a^{2} ln ∣ x ∣

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

= a^{2} ln ∣ x ∣ - \frac{x ^{2}}{2}

Add a constant to the solution

= a^{2} ln ∣ x ∣ - \frac{x ^{2}}{2} + C

2 y sin (x) - 4

\frac{1}{( v ^{2} + 3 )}

\frac{1}{x - x ^{2}}

cot^{3} (x)

4^{3 x}

What is the integral of ((a^2-x^2))/x ?
The integral of ((a^2-x^2))/x is a^2ln|x|-(x^2)/2+C