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

The integral of (sqrt(a^2-x^2))/(x^2) is -(sqrt(a^2-x^2))/x-arcsin(x/a)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(a^2-x^2))/(x^2)

\int \frac{a ^{2} - x ^{2}}{x ^{2}} d x

- \frac{a ^{2} - x ^{2}}{x} - arcsin (\frac{x}{a}) + C

Solution steps

\int \frac{a ^{2} - x ^{2}}{x ^{2}} d x

Apply Integration By Parts

: - \frac{a ^{2} - x ^{2}}{x} - \int \frac{1}{a ^{2} - x ^{2}} d x

= - \frac{a ^{2} - x ^{2}}{x} - \int \frac{1}{a ^{2} - x ^{2}} d x

\int \frac{1}{a ^{2} - x ^{2}} d x = arcsin (\frac{x}{a})

= - \frac{a ^{2} - x ^{2}}{x} - arcsin (\frac{x}{a})

Add a constant to the solution

= - \frac{a ^{2} - x ^{2}}{x} - arcsin (\frac{x}{a}) + C

y = 11 x, y = x^{2} - 12

\int_{1}^{4} (x^{2}) d x

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

n = 0 \sum \infty 0. 4^{n}

\frac{d}{d x} (e^{- x^{2} + 7 x})

What is the integral of (sqrt(a^2-x^2))/(x^2) ?
The integral of (sqrt(a^2-x^2))/(x^2) is -(sqrt(a^2-x^2))/x-arcsin(x/a)+C