What is the integral of 2/(sqrt(25-100x^2)) ?

The integral of 2/(sqrt(25-100x^2)) is 1/5 arcsin(2x)+C

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integral of 2/(sqrt(25-100x^2))

\int \frac{2}{25 - 100 x ^{2}} d x

\frac{1}{5} arcsin (2 x) + C

Solution steps

\int \frac{2}{25 - 100 x ^{2}} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{25 - 100 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{10} d u

= 2 \cdot \int \frac{1}{10} d u

Take the constant out:

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

= 2 \cdot \frac{1}{10} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot \frac{1}{10} \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{10}{5} x)

= 2 \cdot \frac{1}{10} \cdot 1 \cdot arcsin (\frac{10}{5} x)

Simplify

2 \cdot \frac{1}{10} \cdot 1 \cdot arcsin (\frac{10}{5} x) : \frac{1}{5} arcsin (2 x)

= \frac{1}{5} arcsin (2 x)

Add a constant to the solution

= \frac{1}{5} arcsin (2 x) + C

y = \frac{arctan ( 2 x )}{x}

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

\int_{2}^{3} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

h \to 0 lim (- 2 x - h + 8)

x \to 1 lim (\frac{x + 1}{x ^{3} - 1})

What is the integral of 2/(sqrt(25-100x^2)) ?
The integral of 2/(sqrt(25-100x^2)) is 1/5 arcsin(2x)+C