What is the integral of 1/(sqrt(x^2+11)) ?

The integral of 1/(sqrt(x^2+11)) is ln| 1/(sqrt(11))x+sqrt(1/11 (11+x^2))|+C

Popular >

integral of 1/(sqrt(x^2+11))

\int \frac{1}{x ^{2} + 11} d x

ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2}) + C

Solution steps

\int \frac{1}{x ^{2} + 11} d x

Apply Trigonometric Substitution

: \int sec (u) d u

= \int sec (u) d u

Use the common integral:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= ln ∣ tan (u) + sec (u) ∣

Substitute back

u = arctan (\frac{1}{11} x)

= ln tan (arctan (\frac{1}{11} x)) + sec (arctan (\frac{1}{11} x))

Simplify

ln tan (arctan (\frac{1}{11} x)) + sec (arctan (\frac{1}{11} x)) : ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2})

= ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2})

Add a constant to the solution

= ln \frac{1}{11} x + \frac{1}{11} (11 + x^{2}) + C

\frac{d P}{d t} = (\frac{P}{5}) (lo g_{e} (\frac{3000}{P}))

\frac{\partial}{\partial x} (6 y^{5} sin (3 x))

y = (x^{2} + 5 x + 2)^{3}

x \to \frac{c}{2 ^{-}} lim ([2 x - 4])

(y^{2} + x y^{2}) y^{^{'}} = 1

What is the integral of 1/(sqrt(x^2+11)) ?
The integral of 1/(sqrt(x^2+11)) is ln| 1/(sqrt(11))x+sqrt(1/11 (11+x^2))|+C