What is the integral of (sqrt(a^2-x^2))/(x^4) ?

The integral of (sqrt(a^2-x^2))/(x^4) is -(sqrt(a^2-x^2))/(3x^3)+(sqrt(a^2-x^2))/(3a^2x)+C

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integral of (sqrt(a^2-x^2))/(x^4)

\int \frac{a ^{2} - x ^{2}}{x ^{4}} d x

- \frac{a ^{2} - x ^{2}}{3 x ^{3}} + \frac{a ^{2} - x ^{2}}{3 a ^{2} x} + C

Solution steps

\int \frac{a ^{2} - x ^{2}}{x ^{4}} d x

Apply Integration By Parts

: - \frac{a ^{2} - x ^{2}}{3 x ^{3}} - \int \frac{1}{3 x ^{2} - x ^{2} + a ^{2}} d x

= - \frac{a ^{2} - x ^{2}}{3 x ^{3}} - \int \frac{1}{3 x ^{2} - x ^{2} + a ^{2}} d x

\int \frac{1}{3 x ^{2} - x ^{2} + a ^{2}} d x = - \frac{a ^{2} - x ^{2}}{3 a ^{2} x}

= - \frac{a ^{2} - x ^{2}}{3 x ^{3}} - (- \frac{a ^{2} - x ^{2}}{3 a ^{2} x})

Simplify

= - \frac{a ^{2} - x ^{2}}{3 x ^{3}} + \frac{a ^{2} - x ^{2}}{3 a ^{2} x}

Add a constant to the solution

= - \frac{a ^{2} - x ^{2}}{3 x ^{3}} + \frac{a ^{2} - x ^{2}}{3 a ^{2} x} + C

x \to 2 lim (x + 3)

y = ln (lo g_{e} (2 x))

n = 1 \sum \infty (x - 2)^{n}

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

\frac{d}{d x} (\frac{4 x ^{3}}{3} - x)

What is the integral of (sqrt(a^2-x^2))/(x^4) ?
The integral of (sqrt(a^2-x^2))/(x^4) is -(sqrt(a^2-x^2))/(3x^3)+(sqrt(a^2-x^2))/(3a^2x)+C