What is the integral of (23)/((1-x^2)^{3/2)} ?

The integral of (23)/((1-x^2)^{3/2)} is (23x)/((1-x^2)^{1/2)}+C

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integral of (23)/((1-x^2)^{3/2)}

\int \frac{23}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{23 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}} + C

Solution steps

\int \frac{23}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

Take the constant out:

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

= 23 \cdot \int \frac{1}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

Apply Trigonometric Substitution

: \int sec^{2} (u) d u

= 23 \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= 23 tan (u)

Substitute back

u = arcsin (x)

= 23 tan (arcsin (x))

Simplify

23 tan (arcsin (x)) : \frac{23 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

= \frac{23 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{23 x}{( 1 - x ^{2} ) ^{\frac{1}{2}}} + C

x \to 5 - lim (\frac{8 x}{x - 5})

\frac{d}{d t} (b sin (t))

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

\int sin^{3} (x) cos^{10} (x) d x

\frac{d}{d x} (\frac{2}{5} x^{\frac{5}{2}})

What is the integral of (23)/((1-x^2)^{3/2)} ?
The integral of (23)/((1-x^2)^{3/2)} is (23x)/((1-x^2)^{1/2)}+C