What is the integral of (7sqrt(x^2-1))/(x^2) ?

The integral of (7sqrt(x^2-1))/(x^2) is 7(-(sqrt(x^2-1))/x+ln|sqrt(x^2-1)+x|)+C

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integral of (7sqrt(x^2-1))/(x^2)

\int \frac{7 x ^{2} - 1}{x ^{2}} d x

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

Solution steps

\int \frac{7 x ^{2} - 1}{x ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int \frac{x ^{2} - 1}{x ^{2}} d x

Apply Integration By Parts

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

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

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

= 7 (- \frac{x ^{2} - 1}{x} - (- ln x^{2} - 1 + x))

Simplify

= 7 (- \frac{x ^{2} - 1}{x} + ln x^{2} - 1 + x)

Add a constant to the solution

= 7 (- \frac{x ^{2} - 1}{x} + ln x^{2} - 1 + x) + C

f (x) = \frac{1}{x}, at x = 1

\frac{\partial}{\partial x} (\frac{x ^{2}}{x + 1})

\frac{d}{d x} (5 x^{2} + 3 x)

\int \frac{x + 5}{x ^{2} + x - 2} d x

x^{2} + 3 x - 1

What is the integral of (7sqrt(x^2-1))/(x^2) ?
The integral of (7sqrt(x^2-1))/(x^2) is 7(-(sqrt(x^2-1))/x+ln|sqrt(x^2-1)+x|)+C