The expression 1-4 x-1-1-4 x-1-2-7-1-4 x-1-2-7- is a polynomial in x of degree

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The expressio...

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The expression $\frac{1}{\sqrt{4 x + 1}}$ $[{[\frac{1 + \sqrt{4 x + 1}}{2}]}^{7} - {[\frac{1 - \sqrt{4 x + 1}}{2}]}^{7}]$ is a polynomial in x of degree

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\frac{1}{\sqrt{4 x + 1}} ⎡ ⎣ {[\frac{1 + \sqrt{4 x + 1}}{2}]}^{7} - {[\frac{1 + \sqrt{4 x + 1}}{2}]}^{7} ⎤ ⎦

\frac{1}{\sqrt{4 x + 1}} ⎡ ⎣ {(\frac{1 + \sqrt{4 x + 1}}{2})}^{7} - {(\frac{1 - \sqrt{4 x + 1}}{2})}^{7} ⎤ ⎦

\frac{1}{\sqrt{4 x + 1}} ⎡ ⎣ {(\frac{1 + \sqrt{4 x + 1}}{2})}^{7} - {(\frac{1 - \sqrt{4 x + 1}}{2})}^{7} ⎤ ⎦

4 x^{2} + 3 x - 7

x = 1

\int (x + 3) \sqrt{3 - 4 x - x^{2}} d x = \frac{- 1}{3} {(3 - 4 x - x^{2})}^{3 / 2} + \frac{(x + 2) \sqrt{3 - 4 x - x^{2}}}{2} + \frac{7}{2} {sin}^{- 1} \frac{(x + 2)}{\sqrt{7}} + C

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