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Question

Mathematics Question on Definite Integral

∫5−2x+x2 dx=\int\sqrt{5-2x+x^2}\ dx=

A

x−125+2x+x2+2log⁡∣(x−1)+5+2x+x2∣+C\frac{x-1}{2}\sqrt{5+2x+x^2}+2\log|(x-1)+\sqrt{5+2x+x^2}|+C

B

x−125−2x+x2+2log⁡∣(x−1)+x2+2x+5∣+C\frac{x-1}{2}\sqrt{5-2x+x^2}+2\log|(x-1)+\sqrt{x^2+2x+5}|+C

C

x−125−2x+x2+2log⁡∣(x−1)+5−2x+x2∣+C\frac{x-1}{2}\sqrt{5-2x+x^2}+2\log|(x-1)+\sqrt{5-2x+x^2}|+C

D

x25−2x+x2+4log⁡∣(x−1)+x2−2x+5∣+C\frac{x}{2}\sqrt{5-2x+x^2}+4\log|(x-1)+\sqrt{x^2-2x+5}|+C

Answer

x−125−2x+x2+2log⁡∣(x−1)+5−2x+x2∣+C\frac{x-1}{2}\sqrt{5-2x+x^2}+2\log|(x-1)+\sqrt{5-2x+x^2}|+C

Explanation

Solution

The correct answer is (C) : x−125−2x+x2+2log⁡∣(x−1)+5−2x+x2∣+C\frac{x-1}{2}\sqrt{5-2x+x^2}+2\log|(x-1)+\sqrt{5-2x+x^2}|+C.