Integrate 1 − x 2 + 3 x + 1 with respect to x.

Multiply&nbsp;1-x2+3x+1&nbsp;by&nbsp;-x2+3x+1-x2+3x+1.1-x2+3x+1⋅-x2+3x+1-x2+3x+1Combine and simplify the denominator.-x2+3x+1-x2+3x+1Factor&nbsp;-1&nbsp;out of&nbsp;-x2.-x2+3x+1-(x2)+3x+1Factor&nbsp;-1&nbsp;out of&nbsp;3x.-x2+3x+1-(x2)-(-3x)+1Factor&nbsp;-1&nbsp;out of&nbsp;-(x2)-(-3x).-x2+3x+1-(x2-3x)+1Rewrite&nbsp;1&nbsp;as&nbsp;-1(-1).-x2+3x+1-(x2-3x)-1(-1)Factor&nbsp;-1&nbsp;out of&nbsp;-(x2-3x)-1(-1).-x2+3x+1-(x2-3x-1)Rewrite negatives.--x2+3x+1x2-3x-1&nbsp;

Find out the answer to "Integrate 1 − x 2 + 3 x..."

dumnealorjavgj

Answered question

2022-05-12

Integrate

\frac{1}{\sqrt{- x^{2} + 3 x + 1}}

with respect to x.

Answer & Explanation

Darion Sexton

Beginner2022-05-13Added 14 answers

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

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

Combine and simplify the denominator.

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

Factor $- 1$ out of $- x^{2}$ .

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

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

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

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

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

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

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

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

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

Rewrite negatives.

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

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