What is the integral of (sqrt(x^2+25))/(x^2) ?

The integral of (sqrt(x^2+25))/(x^2) is -(sqrt(x^2+25))/x+ln(1/5 |x+sqrt(25+x^2)|)+C

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integral of (sqrt(x^2+25))/(x^2)

\int \frac{x ^{2} + 25}{x ^{2}} d x

- \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2}) + C

Solution steps

\int \frac{x ^{2} + 25}{x ^{2}} d x

Apply Integration By Parts

: - \frac{x ^{2} + 25}{x} - \int - \frac{1}{x ^{2} + 25} d x

= - \frac{x ^{2} + 25}{x} - \int - \frac{1}{x ^{2} + 25} d x

\int - \frac{1}{x ^{2} + 25} d x = - ln (\frac{1}{5} x + 25 + x^{2})

= - \frac{x ^{2} + 25}{x} - (- ln (\frac{1}{5} x + 25 + x^{2}))

Simplify

= - \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2})

Add a constant to the solution

= - \frac{x ^{2} + 25}{x} + ln (\frac{1}{5} x + 25 + x^{2}) + C

x = y^{2}, x = 2 - y

f (x) = \frac{- 4 x}{x ^{2} + 1}, (- 1, 2)

cos (θ^{2})

\int x (x^{2} + 4)^{5} d x

\frac{\partial}{\partial x} (e^{y x})

What is the integral of (sqrt(x^2+25))/(x^2) ?
The integral of (sqrt(x^2+25))/(x^2) is -(sqrt(x^2+25))/x+ln(1/5 |x+sqrt(25+x^2)|)+C