What is the integral of (x^6)/(sqrt(1-x^{14))} ?

The integral of (x^6)/(sqrt(1-x^{14))} is 1/7 arcsin(x^7)+C

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integral of (x^6)/(sqrt(1-x^{14))}

\int \frac{x ^{6}}{1 - x ^{14}} d x

\frac{1}{7} arcsin (x^{7}) + C

Solution steps

\int \frac{x ^{6}}{1 - x ^{14}} d x

Apply u-substitution

: \int \frac{1}{7 1 - u ^{2}} d u

= \int \frac{1}{7 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}{7} \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}{7} arcsin (u)

Substitute back

u = x^{7}

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

Add a constant to the solution

= \frac{1}{7} arcsin (x^{7}) + C

\int 3 cot^{4} (x) d x

\frac{d}{d x} (5 x - 1)

f (x) = x^{2} - 3 x, at x = 1

\int (12 - 3 t^{2}) d t

\frac{2 s}{( s + 3 ) ^{2} + 7}

What is the integral of (x^6)/(sqrt(1-x^{14))} ?
The integral of (x^6)/(sqrt(1-x^{14))} is 1/7 arcsin(x^7)+C