What is the integral of 3/(sqrt(25-x^2)) ?

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

Popular >

integral of 3/(sqrt(25-x^2))

\int \frac{3}{25 - x ^{2}} d x

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

Solution steps

\int \frac{3}{25 - x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{1}{25 - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= 3 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 3 \cdot 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (arcsec (x))

y^{^{''}} + x^{2} y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 2

f (x) = \frac{x}{x + 5}

\int \frac{1}{8 x + 3} d x

\int - \frac{1}{12 - x} d x

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