What is the integral of (sqrt(y^2-121))/y ?

The integral of (sqrt(y^2-121))/y is -11arcsec(1/11 y)+sqrt(y^2-121)+C

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integral of (sqrt(y^2-121))/y

\int \frac{y ^{2} - 121}{y} d y

- 11 arcsec (\frac{1}{11} y) + y^{2} - 121 + C

Solution steps

\int \frac{y ^{2} - 121}{y} d y

Apply Trigonometric Substitution

: \int 11 tan^{2} (u) d u

= \int 11 tan^{2} (u) d u

Take the constant out:

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

= 11 \cdot \int tan^{2} (u) d u

Rewrite using trig identities

= 11 \cdot \int - 1 + sec^{2} (u) d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 11 (- \int 1 d u + \int sec^{2} (u) d u)

\int 1 d u = u

\int sec^{2} (u) d u = tan (u)

= 11 (- u + tan (u))

Substitute back

u = arcsec (\frac{1}{11} y)

= 11 (- arcsec (\frac{1}{11} y) + tan (arcsec (\frac{1}{11} y)))

Simplify

11 (- arcsec (\frac{1}{11} y) + tan (arcsec (\frac{1}{11} y))) : - 11 arcsec (\frac{1}{11} y) + y^{2} - 121

= - 11 arcsec (\frac{1}{11} y) + y^{2} - 121

Add a constant to the solution

= - 11 arcsec (\frac{1}{11} y) + y^{2} - 121 + C

lo g_{10} (x)

\frac{d}{d x} (- \frac{3 x}{2 y})

\int e^{- x} cos (6 x) d x

\frac{d y}{d x} = \frac{x}{y ( x ^{2} + 1 )}

(2010, 73.1), (2000, 71.3)

What is the integral of (sqrt(y^2-121))/y ?
The integral of (sqrt(y^2-121))/y is -11arcsec(1/11 y)+sqrt(y^2-121)+C