What is the integral of 1/(sqrt(361-x^2)) ?

The integral of 1/(sqrt(361-x^2)) is arcsin(1/19 x)+C

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integral of 1/(sqrt(361-x^2))

\int \frac{1}{361 - x ^{2}} d x

arcsin (\frac{1}{19} x) + C

Solution steps

\int \frac{1}{361 - 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}{19} x)

= 1 \cdot arcsin (\frac{1}{19} x)

Simplify

= arcsin (\frac{1}{19} x)

Add a constant to the solution

= arcsin (\frac{1}{19} x) + C

\frac{d y}{d x} - \frac{y}{x} = x e^{x}, y (1) = e - 1

x \to \infty lim (\frac{1}{4 x})

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

\frac{d y}{d x} = \frac{x}{- y}

y = arcsin (2 x + 1)

What is the integral of 1/(sqrt(361-x^2)) ?
The integral of 1/(sqrt(361-x^2)) is arcsin(1/19 x)+C