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Popular >

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

Solution

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

Solution

- \frac{1}{2} ln a^{2} - x^{2} + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2 u} d u

= \int - \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} ln ∣ u ∣

Substitute back

u = a^{2} - x^{2}

= - \frac{1}{2} ln a^{2} - x^{2}

Add a constant to the solution

= - \frac{1}{2} ln a^{2} - x^{2} + C

Popular Examples

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

\int (ln (\frac{2 a}{x}))^{2} d x

integral of (5x-5)/(x^2+x-6)

\int \frac{5 x - 5}{x ^{2} + x - 6} d x

integral of 1/(sqrt(x)+5)

\int \frac{1}{x + 5} d x

integral of sqrt(144-16x^2)

\int 144 - 16 x^{2} d x

integral of xartan(x)

\int x a r tan (x) d x

Frequently Asked Questions (FAQ)

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