What is the integral of (17)/(sqrt(9-25x^2)) ?

The integral of (17)/(sqrt(9-25x^2)) is 17/5 arcsin(5/3 x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (17)/(sqrt(9-25x^2))

\int \frac{17}{9 - 25 x ^{2}} d x

\frac{17}{5} arcsin (\frac{5}{3} x) + C

Solution steps

\int \frac{17}{9 - 25 x ^{2}} d x

Take the constant out:

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

= 17 \cdot \int \frac{1}{9 - 25 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{5} d u

= 17 \cdot \int \frac{1}{5} d u

Take the constant out:

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

= 17 \cdot \frac{1}{5} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 17 \cdot \frac{1}{5} \cdot 1 \cdot u

Substitute back

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

= 17 \cdot \frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{3} x)

Simplify

17 \cdot \frac{1}{5} \cdot 1 \cdot arcsin (\frac{5}{3} x) : \frac{17}{5} arcsin (\frac{5}{3} x)

= \frac{17}{5} arcsin (\frac{5}{3} x)

Add a constant to the solution

= \frac{17}{5} arcsin (\frac{5}{3} x) + C

\int e^{3 y} y d y

\frac{d}{d x} (\frac{x - x ^{2}}{x - 1})

\frac{d y}{d x} = 2 y x

\int \frac{2 ^{t}}{2 ^{t} + 3} d t

\frac{\partial}{\partial x} (7 e^{x^{8} y})

What is the integral of (17)/(sqrt(9-25x^2)) ?
The integral of (17)/(sqrt(9-25x^2)) is 17/5 arcsin(5/3 x)+C