What is the integral of 1/(sqrt(121+x^2)) ?

The integral of 1/(sqrt(121+x^2)) is ln(1/11 |x+sqrt(121+x^2)|)+C

Popular >

integral of 1/(sqrt(121+x^2))

\int \frac{1}{121 + x ^{2}} d x

ln (\frac{1}{11} x + 121 + x^{2}) + C

Solution steps

\int \frac{1}{121 + x ^{2}} 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 + 121 + x^{2})

= ln (\frac{1}{11} x + 121 + x^{2})

Add a constant to the solution

= ln (\frac{1}{11} x + 121 + x^{2}) + C

x \to 2 + lim (\frac{x - 3}{x - 2})

\int \frac{2}{sin ( x )} d x

\frac{\partial}{\partial x} (x^{0.25} y^{0.75})

y^{^{'}} + sin (t) y = sin (t), y (0) = 3

\int (- 2 y) d y

What is the integral of 1/(sqrt(121+x^2)) ?
The integral of 1/(sqrt(121+x^2)) is ln(1/11 |x+sqrt(121+x^2)|)+C