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

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

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

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

arcsin (\frac{1}{11} x) + C

Solution steps

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

Apply Trigonometric Substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

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

= 1 \cdot arcsin (\frac{1}{11} x)

Simplify

= arcsin (\frac{1}{11} x)

Add a constant to the solution

= arcsin (\frac{1}{11} x) + C

\frac{d}{d x} (\frac{x ^{2} + 1}{x + 4})

7 x^{2} y^{^{''}} + 15 x y^{^{'}} + y = 0

(x^{3} - 6 x^{2} + 2 x - 2)^{^{'}}

sin (x) + \frac{1}{2} cot (x)

y = \frac{ln ( x )}{1 + ln ( x )}

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