Evaluate ∫ 1 − 3 t 2 + 3 t + 1 d t.

Multiply&nbsp;1-3t2+3t+1&nbsp;by&nbsp;-3t2+3t+1-3t2+3t+1.1-3t2+3t+1⋅-3t2+3t+1-3t2+3t+1Combine and simplify the denominator.-3t2+3t+1-3t2+3t+1Factor&nbsp;-1&nbsp;out of&nbsp;-3t2.-3t2+3t+1-(3t2)+3t+1Factor&nbsp;-1&nbsp;out of&nbsp;3t.-3t2+3t+1-(3t2)-(-3t)+1Factor&nbsp;-1&nbsp;out of&nbsp;-(3t2)-(-3t).-3t2+3t+1-(3t2-3t)+1Rewrite&nbsp;1&nbsp;as&nbsp;-1(-1).-3t2+3t+1-(3t2-3t)-1(-1)Factor&nbsp;-1&nbsp;out of&nbsp;-(3t2-3t)-1(-1).-3t2+3t+1-(3t2-3t-1)Rewrite negatives.&nbsp;--3t2+3t+13t2-3t-1&nbsp;

Check the solution to "Evaluate ∫ 1 − 3 t 2 +..."

Thaddeus Sanders

Answered question

2022-05-13

Evaluate

\int \frac{1}{\sqrt{- 3 t^{2} + 3 t + 1}} d t

Answer & Explanation

Jaylon Richmond

Beginner2022-05-14Added 10 answers

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

$\frac{1}{\sqrt{- 3 t^{2} + 3 t + 1}} \cdot \frac{\sqrt{- 3 t^{2} + 3 t + 1}}{\sqrt{- 3 t^{2} + 3 t + 1}}$

Combine and simplify the denominator.

$\frac{\sqrt{- 3 t^{2} + 3 t + 1}}{- 3 t^{2} + 3 t + 1}$

Factor $- 1$ out of $- 3 t^{2}$ .

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

Factor $- 1$ out of $3 t$ .

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

Factor $- 1$ out of $- (3 t^{2}) - (- 3 t)$ .

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

Rewrite $1$ as $- 1 (- 1)$ .

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

Factor $- 1$ out of $- (3 t^{2} - 3 t) - 1 (- 1)$ .

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

Rewrite negatives.

$- \frac{\sqrt{- 3 t^{2} + 3 t + 1}}{3 t^{2} - 3 t - 1}$

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