Solve integral of t^2/(sqrt 1-t^6)dt

Evaluate

\int e g r a l o f \times \frac{t ^{2}}{1 - t ^{6}} d t

Simplify the root

\int e g r a l o f \times \frac{t ^{2}}{1 - t ^{6}} d t

Use the property of integral \int k f (x) d x = k \int f (x) d x

e g r a l o f \times \int \frac{t ^{2}}{1 - t ^{6}} d t

Use the substitution d t = \frac{1}{3 t ^{2}} d v to transform the integral

More Steps

e g r a l o f \times \int \frac{t ^{2}}{1 - t ^{6}} \times \frac{1}{3 t ^{2}} d v

Simplify

More Steps

e g r a l o f \times \int \frac{1}{3 - 3 ( t ^{3} ) ^{2}} d v

Use the substitution v = t^{3} to transform the integral

e g r a l o f \times \int \frac{1}{3 - 3 v ^{2}} d v

Rewrite the expression

e g r a l o f \times \int \frac{1}{3} \times \frac{1}{1 - v ^{2}} d v

Use the property of integral \int k f (x) d x = k \int f (x) d x

e g r a l o f \times \frac{1}{3} \times \int \frac{1}{1 - v ^{2}} d v

Multiply the numbers

\frac{e g r a l o f}{3} \times \int \frac{1}{1 - v ^{2}} d v

Use the property of integral \int \frac{1}{a ^{2} - x ^{2}} d x = \frac{1}{2 a} ln \frac{x + a}{x - a}

\frac{e g r a l o f}{3} \times \frac{1}{2} ln (\frac{v + 1}{v - 1})

Multiply the terms

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\frac{e g r a l o f}{6} ln (\frac{v + 1}{v - 1})

Substitute back

\frac{e g r a l o f}{6} ln (\frac{t ^{3} + 1}{t ^{3} - 1})

Simplify the expression

\frac{e}{6} g r a l o f ln (\frac{t ^{3} + 1}{t ^{3} - 1})

Solution

\frac{e}{6} g r a l o f ln (\frac{t ^{3} + 1}{t ^{3} - 1}) + C, C \in R

Evaluate the integral