What is the integral of (x^4)/(sqrt(1-x^{10))} ?

The integral of (x^4)/(sqrt(1-x^{10))} is 1/5 arcsin(x^5)+C

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integral of (x^4)/(sqrt(1-x^{10))}

\int \frac{x ^{4}}{1 - x ^{10}} d x

\frac{1}{5} arcsin (x^{5}) + C

Solution steps

\int \frac{x ^{4}}{1 - x ^{10}} d x

Apply u-substitution

: \int \frac{1}{5 1 - u ^{2}} d u

= \int \frac{1}{5 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}{5} \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}{5} arcsin (u)

Substitute back

u = x^{5}

= \frac{1}{5} arcsin (x^{5})

Add a constant to the solution

= \frac{1}{5} arcsin (x^{5}) + C

x \to \infty lim (e x)

\int_{1}^{2} \frac{2}{x ^{3} + 4 x} d x

\frac{\partial}{\partial y} (x^{2} \cdot y^{2})

y^{^{''}} - 7 y^{^{'}} - 18 y = 0

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

What is the integral of (x^4)/(sqrt(1-x^{10))} ?
The integral of (x^4)/(sqrt(1-x^{10))} is 1/5 arcsin(x^5)+C