What is the integral of (13)/(sqrt(25-9x^2)) ?

The integral of (13)/(sqrt(25-9x^2)) is 13/3 arcsin(3/5 x)+C

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integral of (13)/(sqrt(25-9x^2))

\int \frac{13}{25 - 9 x ^{2}} d x

\frac{13}{3} arcsin (\frac{3}{5} x) + C

Solution steps

\int \frac{13}{25 - 9 x ^{2}} d x

Take the constant out:

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

= 13 \cdot \int \frac{1}{25 - 9 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{3} d u

= 13 \cdot \int \frac{1}{3} d u

Take the constant out:

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

= 13 \cdot \frac{1}{3} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 13 \cdot \frac{1}{3} \cdot 1 \cdot u

Substitute back

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

= 13 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (\frac{3}{5} x)

Simplify

13 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (\frac{3}{5} x) : \frac{13}{3} arcsin (\frac{3}{5} x)

= \frac{13}{3} arcsin (\frac{3}{5} x)

Add a constant to the solution

= \frac{13}{3} arcsin (\frac{3}{5} x) + C

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\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}

\int (sin (x) - 2 e^{x} + 3 x) d x

\int y^{2} (\frac{1}{y ^{5}} + \frac{y ^{4}}{2}) d y

What is the integral of (13)/(sqrt(25-9x^2)) ?
The integral of (13)/(sqrt(25-9x^2)) is 13/3 arcsin(3/5 x)+C