What is the integral of 1/(sqrt(9-25x^2)) ?

The integral of 1/(sqrt(9-25x^2)) is 1/5 arcsin(5/3 x)+C

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integral of 1/(sqrt(9-25x^2))

\int \frac{1}{9 - 25 x ^{2}} d x

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

Solution steps

\int \frac{1}{9 - 25 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{5} d u

= \int \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{5} \cdot 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{1}{y} sin (\frac{x}{y}) + x d x

\frac{d}{d x} (b x e^{2 x y})

\int 1 + \frac{9 x}{4} d x

\frac{\partial}{\partial y} (ln (5 x + 4 y))

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

What is the integral of 1/(sqrt(9-25x^2)) ?
The integral of 1/(sqrt(9-25x^2)) is 1/5 arcsin(5/3 x)+C