What is the integral of 1/(sqrt(144-x^2)) ?

The integral of 1/(sqrt(144-x^2)) is arcsin(1/12 x)+C

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integral of 1/(sqrt(144-x^2))

\int \frac{1}{144 - x ^{2}} d x

arcsin (\frac{1}{12} x) + C

Solution steps

\int \frac{1}{144 - 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}{12} x)

= 1 \cdot arcsin (\frac{1}{12} x)

Simplify

= arcsin (\frac{1}{12} x)

Add a constant to the solution

= arcsin (\frac{1}{12} x) + C

\int arccot (8 y) d y

\int \frac{1 - x}{1 + x} d x

\int 58

\int_{1}^{5} 1 + (3)^{2} d x

\int_{0}^{t} e^{- 2 t} sin (5 t) d t

What is the integral of 1/(sqrt(144-x^2)) ?
The integral of 1/(sqrt(144-x^2)) is arcsin(1/12 x)+C