What is the integral of 1/(x^2sqrt(4-8x^2)) ?

The integral of 1/(x^2sqrt(4-8x^2)) is -(sqrt(1-2x^2))/(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x^2sqrt(4-8x^2))

\int \frac{1}{x ^{2} 4 - 8 x ^{2}} d x

- \frac{1 - 2 x ^{2}}{2 x} + C

Solution steps

\int \frac{1}{x ^{2} 4 - 8 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{2 sin ^{2} ( u )} d u

= \int \frac{1}{2 sin ^{2} ( u )} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{sin ^{2} ( u )} d u

Use the common integral:

\int \frac{1}{sin ^{2} ( u )} d u = - cot (u)

= \frac{1}{2} (- cot (u))

Substitute back

u = arcsin (\frac{2 2}{2} x)

= \frac{1}{2} (- cot (arcsin (\frac{2 2}{2} x)))

Simplify

\frac{1}{2} (- cot (arcsin (\frac{2 2}{2} x))) : - \frac{1 - 2 x ^{2}}{2 x}

= - \frac{1 - 2 x ^{2}}{2 x}

Add a constant to the solution

= - \frac{1 - 2 x ^{2}}{2 x} + C

\int 6 x^{5} (x^{3} + 2)^{15} d x

\int 2 cos (x) \frac{2 csc ( x )}{cot ( x )} d x

\int \frac{x ^{2}}{( a ^{2} - x ^{2} ) ^{3}} d x

\int (6 x - 9) x^{2} - 3 x + 1 d x

\int (\frac{3}{t} - \frac{2}{t ^{2}}) d t

What is the integral of 1/(x^2sqrt(4-8x^2)) ?
The integral of 1/(x^2sqrt(4-8x^2)) is -(sqrt(1-2x^2))/(2x)+C