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

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

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

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Trigonometric Substitution

: \int 1 d u

= 2 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 1 \cdot u

Substitute back

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

= 2 \cdot 1 \cdot arcsin (\frac{1}{5} x)

Simplify

= 2 arcsin (\frac{1}{5} x)

Add a constant to the solution

= 2 arcsin (\frac{1}{5} x) + C

\frac{s}{s ^{2} + 2 s + 4}

\int + ln (x) d x

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.6 y), y (1) = 0.9

x \to 4 lim (∣ x ∣ - 3^{x})

\int_{0}^{2 π} x^{2} sin (n x) d x

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