What is the integral of 1/(sqrt(1-\frac{(x^2)){64)}} ?

The integral of 1/(sqrt(1-\frac{(x^2)){64)}} is 8arcsin(1/8 x)+C

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integral of 1/(sqrt(1-\frac{(x^2)){64)}}

\int \frac{1}{1 - \frac{( x ^{2} )}{64}} d x

8 arcsin (\frac{1}{8} x) + C

Solution steps

\int \frac{1}{1 - \frac{x ^{2}}{64}} d x

Apply Trigonometric Substitution

: \int 8 d u

= \int 8 d u

Take the constant out:

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

= 8 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 8 \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{1}{8} x)

= 8 \cdot 1 \cdot arcsin (\frac{1}{8} x)

Simplify

= 8 arcsin (\frac{1}{8} x)

Add a constant to the solution

= 8 arcsin (\frac{1}{8} x) + C

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What is the integral of 1/(sqrt(1-\frac{(x^2)){64)}} ?
The integral of 1/(sqrt(1-\frac{(x^2)){64)}} is 8arcsin(1/8 x)+C