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

\int a x - x^{2} d x

\int \frac{cos ^{3} ( x )}{3} d x

\int (1 - 2 x^{2})^{3} (- 4 x) d x

\int 250

\int (2 cosh (x) + x^{4}) d 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