What is the integral of (sqrt(9x^2-49))/(x^4) ?

The integral of (sqrt(9x^2-49))/(x^4) is -(sqrt(9x^2-49))/(3x^3)+(3sqrt(9x^2-49))/(49x)+C

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integral of (sqrt(9x^2-49))/(x^4)

\int \frac{9 x ^{2} - 49}{x ^{4}} d x

- \frac{9 x ^{2} - 49}{3 x ^{3}} + \frac{3 9 x ^{2} - 49}{49 x} + C

Solution steps

\int \frac{9 x ^{2} - 49}{x ^{4}} d x

Apply Integration By Parts

: - \frac{9 x ^{2} - 49}{3 x ^{3}} - \int - \frac{3}{x ^{2} 9 x ^{2} - 49} d x

= - \frac{9 x ^{2} - 49}{3 x ^{3}} - \int - \frac{3}{x ^{2} 9 x ^{2} - 49} d x

\int - \frac{3}{x ^{2} 9 x ^{2} - 49} d x = - \frac{3 9 x ^{2} - 49}{49 x}

= - \frac{9 x ^{2} - 49}{3 x ^{3}} - (- \frac{3 9 x ^{2} - 49}{49 x})

Simplify

= - \frac{9 x ^{2} - 49}{3 x ^{3}} + \frac{3 9 x ^{2} - 49}{49 x}

Add a constant to the solution

= - \frac{9 x ^{2} - 49}{3 x ^{3}} + \frac{3 9 x ^{2} - 49}{49 x} + C

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What is the integral of (sqrt(9x^2-49))/(x^4) ?
The integral of (sqrt(9x^2-49))/(x^4) is -(sqrt(9x^2-49))/(3x^3)+(3sqrt(9x^2-49))/(49x)+C