Get the solution to "Find the indefinite integral ∫t1−t4dt"

Minerva Kline

Answered question

2021-11-08

Find the indefinite integral

\int \frac{t}{\sqrt{1 - t^{4}}} d t

Lible1953

Beginner2021-11-09Added 16 answers

Step 1
Given integral,

\int \frac{t}{\sqrt{1 - t^{4}}} d t

Step 2
Now evaluating the given integral

\int \frac{t}{\sqrt{1 - t^{4}}} d t

= \int \frac{t}{\sqrt{1 - {(t^{2})}^{2}}} d t

Let

t^{2} = x

\Rightarrow 2 t d t = d x

\Rightarrow t d t = \frac{1}{2} d x

Now integral

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

= \frac{1}{2} \int \frac{1}{\sqrt{1 - {(x)}^{2}}} d x

= \frac{1}{2} \sin^{- 1} x + C

= \frac{1}{2} \sin^{- 1} (t^{2}) + C

Step 3
Final answer:

\int \frac{t}{\sqrt{1 - t^{4}}} d t = \frac{1}{2} \sin^{- 1} (t^{2}) + C

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