What is the integral of 1/(sqrt(25-81x^2)) ?

The integral of 1/(sqrt(25-81x^2)) is 1/9 arcsin(9/5 x)+C

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integral of 1/(sqrt(25-81x^2))

\int \frac{1}{25 - 81 x ^{2}} d x

\frac{1}{9} arcsin (\frac{9}{5} x) + C

Solution steps

\int \frac{1}{25 - 81 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{9} d u

= \int \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{9} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{9}{5} x)

= \frac{1}{9} \cdot 1 \cdot arcsin (\frac{9}{5} x)

Simplify

= \frac{1}{9} arcsin (\frac{9}{5} x)

Add a constant to the solution

= \frac{1}{9} arcsin (\frac{9}{5} x) + C

e^{x}, - 1, 2

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{2}} d x

\frac{d}{d x} (\frac{5 - 3 x}{5 + 3 x})

1 \frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 2 y = 0

\int_{9}^{10} x x - 9 d x

What is the integral of 1/(sqrt(25-81x^2)) ?
The integral of 1/(sqrt(25-81x^2)) is 1/9 arcsin(9/5 x)+C