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

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

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

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

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

Solution steps

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

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 = t^{7}

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

Add a constant to the solution

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

x \to a + lim (g (x))

\int x^{2} + 3 x + 2 d x

t - e^{- 3 t}

\frac{\partial}{\partial x} (\frac{- 3}{y - 3 x})

2 x^{2} + x - 1, at a = 0

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