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

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

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integral of 1/(sqrt(1-25t^2))

\int \frac{1}{1 - 25 t ^{2}} d t

\frac{1}{5} arcsin (5 t) + C

Solution steps

\int \frac{1}{1 - 25 t ^{2}} d t

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 (5 t)

= \frac{1}{5} \cdot 1 \cdot arcsin (5 t)

Simplify

= \frac{1}{5} arcsin (5 t)

Add a constant to the solution

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

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