Find the integral: ∫ − 2 − x 2 − 5 x + 1 d x.

Multiply&nbsp;2-x2-5x+1&nbsp;by&nbsp;-x2-5x+1-x2-5x+1.-(2-x2-5x+1⋅-x2-5x+1-x2-5x+1)Combine and simplify the denominator.-2-x2-5x+1-x2-5x+1Factor&nbsp;-1&nbsp;out of&nbsp;-x2.-2-x2-5x+1-(x2)-5x+1Factor&nbsp;-1&nbsp;out of&nbsp;-5x.-2-x2-5x+1-(x2)-(5x)+1Factor&nbsp;-1&nbsp;out of&nbsp;-(x2)-(5x).-2-x2-5x+1-(x2+5x)+1Rewrite&nbsp;1&nbsp;as&nbsp;-1(-1).-2-x2-5x+1-(x2+5x)-1(-1)Factor&nbsp;-1&nbsp;out of&nbsp;-(x2+5x)-1(-1).-2-x2-5x+1-(x2+5x-1)Simplify the expression.2-x2-5x+1x2+5x-1&nbsp;

Check the solution to "Find the integral: ∫ − 2 − x..."

poklanima5lqp3

Answered question

2022-05-12

Find the integral:

\int - \frac{2}{\sqrt{- x^{2} - 5 x + 1}} ﻿ d x

Answer & Explanation

arbotsck8sg

Beginner2022-05-13Added 22 answers

Multiply $\frac{2}{\sqrt{- x^{2} - 5 x + 1}}$ by $\frac{\sqrt{- x^{2} - 5 x + 1}}{\sqrt{- x^{2} - 5 x + 1}}$ .

$- (\frac{2}{\sqrt{- x^{2} - 5 x + 1}} \cdot \frac{\sqrt{- x^{2} - 5 x + 1}}{\sqrt{- x^{2} - 5 x + 1}})$

Combine and simplify the denominator.

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- x^{2} - 5 x + 1}$

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

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- (x^{2}) - 5 x + 1}$

Factor $- 1$ out of $- 5 x$ .

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- (x^{2}) - (5 x) + 1}$

Factor $- 1$ out of $- (x^{2}) - (5 x)$ .

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- (x^{2} + 5 x) + 1}$

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

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- (x^{2} + 5 x) - 1 (- 1)}$

Factor $- 1$ out of $- (x^{2} + 5 x) - 1 (- 1)$ .

$- \frac{2 \sqrt{- x^{2} - 5 x + 1}}{- (x^{2} + 5 x - 1)}$

Simplify the expression.

$\frac{2 \sqrt{- x^{2} - 5 x + 1}}{x^{2} + 5 x - 1}$

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