What is the integral of 1/(sqrt(5-x^2)) ?

The integral of 1/(sqrt(5-x^2)) is arcsin(1/(sqrt(5))x)+C

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integral of 1/(sqrt(5-x^2))

\int \frac{1}{5 - x ^{2}} d x

arcsin (\frac{1}{5} x) + C

Solution steps

\int \frac{1}{5 - 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}{5} x)

= 1 \cdot arcsin (\frac{1}{5} x)

Simplify

= arcsin (\frac{1}{5} x)

Add a constant to the solution

= arcsin (\frac{1}{5} x) + C

y^{^{''}} + 16 y = 5 csc^{2} (4 t)

\int_{0}^{1} π (1 - x^{3})^{2} d x

\frac{\partial}{\partial x} (e^{x} \cdot sin (y))

\int_{0}^{\frac{1}{2}} (4 x + 3) e^{2 x} d x

\frac{\partial}{\partial x} (\frac{5}{x y})

What is the integral of 1/(sqrt(5-x^2)) ?
The integral of 1/(sqrt(5-x^2)) is arcsin(1/(sqrt(5))x)+C