What is the integral of (-12)/(x^2sqrt(4-x^2)) ?

The integral of (-12)/(x^2sqrt(4-x^2)) is (3sqrt(-x^2+4))/x+C

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integral of (-12)/(x^2sqrt(4-x^2))

\int \frac{- 12}{x ^{2} 4 - x ^{2}} d x

\frac{3 - x ^{2} + 4}{x} + C

Solution steps

\int \frac{- 12}{x ^{2} 4 - x ^{2}} d x

Take the constant out:

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

= - 12 \cdot \int \frac{1}{x ^{2} 4 - x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{cot ( u )}{4 cos ( u ) sin ( u )} d u

= - 12 \cdot \int \frac{cot ( u )}{4 cos ( u ) sin ( u )} d u

Take the constant out:

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

= - 12 \cdot \frac{1}{4} \cdot \int \frac{cot ( u )}{cos ( u ) sin ( u )} d u

Simplify

\frac{cot ( u )}{cos ( u ) sin ( u )} : csc^{2} (u)

= - 12 \cdot \frac{1}{4} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= - 12 \cdot \frac{1}{4} (- cot (u))

Substitute back

u = arcsin (\frac{1}{2} x)

= - 12 \cdot \frac{1}{4} (- cot (arcsin (\frac{1}{2} x)))

Simplify

- 12 \cdot \frac{1}{4} (- cot (arcsin (\frac{1}{2} x))) : \frac{3 - x ^{2} + 4}{x}

= \frac{3 - x ^{2} + 4}{x}

Add a constant to the solution

= \frac{3 - x ^{2} + 4}{x} + C

\frac{\partial}{\partial x} (4 x^{2} + y^{2} - 7 y)

\frac{d}{d x} (\frac{6 x}{x ^{2} + 3})

\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

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

x^{2} - 1

What is the integral of (-12)/(x^2sqrt(4-x^2)) ?
The integral of (-12)/(x^2sqrt(4-x^2)) is (3sqrt(-x^2+4))/x+C