What is the integral of (sqrt(1-25x^2))/(x^2) ?

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

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integral of (sqrt(1-25x^2))/(x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int 3 \frac{cos ( x ) + sin ( x )}{sin ( 2 x )} d x

e^{2 x + 1}

f (x) = 5 x^{- 2}

\int (3 x - 2) e - x d x

f^{^{'}} (x) = 5 e^{x} + 3 x^{2} - 2 x

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