What is the integral of 5/(sqrt(9-x^2)) ?

The integral of 5/(sqrt(9-x^2)) is 5arcsin(1/3 x)+C

Popular >

integral of 5/(sqrt(9-x^2))

\int \frac{5}{9 - x ^{2}} d x

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

Solution steps

\int \frac{5}{9 - x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{9 - x ^{2}} d x

Apply Trigonometric Substitution

: \int 1 d u

= 5 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 1 \cdot u

Substitute back

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (sin (x) + x^{2} e^{y} + 5)

\int x cosh (x^{2}) d x

\frac{d}{d x} (\frac{x}{2 - x})

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

2 (12) (5) + 2 (5) \frac{d y}{d t} = 0

What is the integral of 5/(sqrt(9-x^2)) ?
The integral of 5/(sqrt(9-x^2)) is 5arcsin(1/3 x)+C