What is the integral of (x^3(1))/(sqrt(1-x^8)) ?

The integral of (x^3(1))/(sqrt(1-x^8)) is 1/4 arcsin(x^4)+C

Popular >

integral of (x^3(1))/(sqrt(1-x^8))

\int \frac{x ^{3} ( 1 )}{1 - x ^{8}} d x

\frac{1}{4} arcsin (x^{4}) + C

Solution steps

\int \frac{x ^{3} \cdot 1}{1 - x ^{8}} d x

Simplify

= \int \frac{x ^{3}}{1 - x ^{8}} d x

Apply u-substitution

: \int \frac{1}{4 1 - u ^{2}} d u

= \int \frac{1}{4 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}{4} \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}{4} arcsin (u)

Substitute back

u = x^{4}

= \frac{1}{4} arcsin (x^{4})

Add a constant to the solution

= \frac{1}{4} arcsin (x^{4}) + C

\frac{d}{d t} (- e^{- t} sin (t) + e^{- t} cos (t))

\frac{2 x ^{2}}{5}

x \to 0 lim (\frac{a ^{x} - 1}{x})

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

\frac{d}{d x} ((x - 1)^{- 1})

What is the integral of (x^3(1))/(sqrt(1-x^8)) ?
The integral of (x^3(1))/(sqrt(1-x^8)) is 1/4 arcsin(x^4)+C