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}

Add a constant to the solution

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

\int \frac{7 x ^{2}}{( x + 1 ) ( x ^{2} + 1 )} d x

\frac{d}{d x} (sin (x^{2}))

\frac{\partial}{\partial y} (arcsin (\frac{x}{y}))

e^{x^{2} + 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