Integrate 2 sin − 1 ⁡ ( 6 t ) 3 1 − 36 t 2 with respect to t.

Simplify the denominator.2sin-1(6t)3(1+6t)(1-6t)Multiply&nbsp;2sin-1(6t)3(1+6t)(1-6t)&nbsp;by&nbsp;(1+6t)(1-6t)(1+6t)(1-6t).2sin-1(6t)3(1+6t)(1-6t)⋅(1+6t)(1-6t)(1+6t)(1-6t)Combine and simplify the denominator.2sin-1(6t)(1+6t)(1-6t)3((1+6t)(1-6t))Combine using the product rule for radicals.2(1+6t)(1-6t)sin-1(6t)3(1+6t)(1-6t)Reorder factors in&nbsp;2(1+6t)(1-6t)sin-1(6t)3(1+6t)(1-6t).2sin-1(6t)(1+6t)(1-6t)3(1+6t)(1-6t)&nbsp;

Resolved: "Integrate 2 sin − 1 ⁡ ( 6..."

lifretatox8n

Answered question

2022-04-10

Integrate

\frac{2 \sqrt{\sin^{- 1} (6 t)}}{3 \sqrt{1 - 36 t^{2}}}

with respect to t.

Answer & Explanation

Ayaan Gonzalez

Beginner2022-04-11Added 15 answers

Simplify the denominator.

$\frac{2 \sqrt{\sin^{-1} (6 t)}}{3 \sqrt{(1 + 6 t) (1 - 6 t)}}$

Multiply $\frac{2 \sqrt{\sin^{-1} (6 t)}}{3 \sqrt{(1 + 6 t) (1 - 6 t)}}$ by $\frac{\sqrt{(1 + 6 t) (1 - 6 t)}}{\sqrt{(1 + 6 t) (1 - 6 t)}}$ .

$\frac{2 \sqrt{\sin^{-1} (6 t)}}{3 \sqrt{(1 + 6 t) (1 - 6 t)}} \cdot \frac{\sqrt{(1 + 6 t) (1 - 6 t)}}{\sqrt{(1 + 6 t) (1 - 6 t)}}$

Combine and simplify the denominator.

$\frac{2 \sqrt{\sin^{-1} (6 t)} \sqrt{(1 + 6 t) (1 - 6 t)}}{3 ((1 + 6 t) (1 - 6 t))}$

Combine using the product rule for radicals.

$\frac{2 \sqrt{(1 + 6 t) (1 - 6 t) \sin^{-1} (6 t)}}{3 (1 + 6 t) (1 - 6 t)}$

Reorder factors in $\frac{2 \sqrt{(1 + 6 t) (1 - 6 t) \sin^{-1} (6 t)}}{3 (1 + 6 t) (1 - 6 t)}$ .

$\frac{2 \sqrt{s {in}^{-1} (6 t) (1 + 6 t) (1 - 6 t)}}{3 (1 + 6 t) (1 - 6 t)}$

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