What is the integral of 1/(sqrt(5-9x^2)) ?

The integral of 1/(sqrt(5-9x^2)) is 1/3 arcsin(3/(sqrt(5))x)+C

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integral of 1/(sqrt(5-9x^2))

\int \frac{1}{5 - 9 x ^{2}} d x

\frac{1}{3} arcsin (\frac{3}{5} x) + C

Solution steps

\int \frac{1}{5 - 9 x ^{2}} d x

Apply Trigonometric Substitution

= \int \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{3}{5} x)

= \frac{1}{3} \cdot 1 \cdot arcsin (\frac{3}{5} x)

Simplify

= \frac{1}{3} arcsin (\frac{3}{5} x)

Add a constant to the solution

= \frac{1}{3} arcsin (\frac{3}{5} x) + C

\int (5 x + 2)^{4} d x

\int I n (x + 1) d x

\int x^{\frac{1}{2}} + 9 d x

\int (4 x + 5)^{6} d x

\int x^{\frac{1}{2}} + 1 d x

What is the integral of 1/(sqrt(5-9x^2)) ?
The integral of 1/(sqrt(5-9x^2)) is 1/3 arcsin(3/(sqrt(5))x)+C