What is the integral of (7x^2)/(sqrt(1-x^6)) ?

The integral of (7x^2)/(sqrt(1-x^6)) is 7/3 arcsin(x^3)+C

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integral of (7x^2)/(sqrt(1-x^6))

\int \frac{7 x ^{2}}{1 - x ^{6}} d x

\frac{7}{3} arcsin (x^{3}) + C

Solution steps

\int \frac{7 x ^{2}}{1 - x ^{6}} d x

Take the constant out:

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

= 7 \cdot \int \frac{x ^{2}}{1 - x ^{6}} d x

Apply u-substitution

: \int \frac{1}{3 1 - u ^{2}} d u

= 7 \cdot \int \frac{1}{3 1 - u ^{2}} d u

Take the constant out:

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

= 7 \cdot \frac{1}{3} \cdot \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

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

= 7 \cdot \frac{1}{3} arcsin (u)

Substitute back

u = x^{3}

= 7 \cdot \frac{1}{3} arcsin (x^{3})

Simplify

7 \cdot \frac{1}{3} arcsin (x^{3}) : \frac{7}{3} arcsin (x^{3})

= \frac{7}{3} arcsin (x^{3})

Add a constant to the solution

= \frac{7}{3} arcsin (x^{3}) + C

\frac{d}{d y} (y z)

x \to 2 lim (- x^{2} + 3)

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

\int \frac{1}{( x - 4 ) ln ( x - 4 )} d x

y^{^{''}} + 2 y^{^{'}} - 8 y = 0

What is the integral of (7x^2)/(sqrt(1-x^6)) ?
The integral of (7x^2)/(sqrt(1-x^6)) is 7/3 arcsin(x^3)+C