What is the integral of (x^5)/(sqrt(1-x^{12))} ?

The integral of (x^5)/(sqrt(1-x^{12))} is 1/6 arcsin(x^6)+C

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integral of (x^5)/(sqrt(1-x^{12))}

\int \frac{x ^{5}}{1 - x ^{12}} d x

\frac{1}{6} arcsin (x^{6}) + C

Solution steps

\int \frac{x ^{5}}{1 - x ^{12}} d x

Apply u-substitution

: \int \frac{1}{6 1 - u ^{2}} d u

= \int \frac{1}{6 1 - u ^{2}} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

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

= \frac{1}{6} arcsin (u)

Substitute back

u = x^{6}

= \frac{1}{6} arcsin (x^{6})

Add a constant to the solution

= \frac{1}{6} arcsin (x^{6}) + C

x \to 8 lim \frac{( x ^{\frac{1}{3}} - 2 )}{x - 8}

\frac{d y}{d x}, x y = 32

\int \frac{1}{y ^{6}} d y

f (t) = \frac{4 t}{3}

x \to 0 lim (\frac{1}{2 + 3 x})

What is the integral of (x^5)/(sqrt(1-x^{12))} ?
The integral of (x^5)/(sqrt(1-x^{12))} is 1/6 arcsin(x^6)+C