Integrate the function -x2-4 x-5 d x

Let I =∫√(x^2+4x 5 2^2+2^2)dx=∫√((x+2)^2 5 4)dx =∫√((x+2)^2 (3)^2)dx ⇒ I =x+2/2√(x^2+4x 5) 9/2log |(x+2)+√(x^2+4x 5)|+C [ ∵∫√((x^2 a^2))dx =x/2√(x^2 a^2) a^2 ...

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Byju's Answer

Standard XII

Mathematics

Integration of Irrational Algebraic Fractions - 2

Integrate the...

Question

Integrate the function.
$\int \sqrt{x^{2} + 4 x - 5} d x .$

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Solution

Let $I = \int \sqrt{x^{2} + 4 x - 5 - 2^{2} + 2^{2}} d x = \int \sqrt{(x + 2)^{2} - 5 - 4} d x$
$= \int \sqrt{(x + 2)^{2} - (3)^{2}} d x \Rightarrow I = \frac{x + 2}{2} \sqrt{x^{2} + 4 x - 5} - \frac{9}{2} l o g | (x + 2) + \sqrt{x^{2} + 4 x - 5} | + C [∵ \int \sqrt{(x^{2} - a^{2})} d x = \frac{x}{2} \sqrt{x^{2} - a^{2}} - \frac{a^{2}}{2} l o g | x + \sqrt{x^{2} - a^{2}} |]$

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Q. Solve :

\int \sqrt{x^{2} + 4 x + 5} d x

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Integrate the function. ∫√x2+4x−5dx.

Let I=∫√x2+4x−5−22+22dx=∫√(x+2)2−5−4dx =∫√(x+2)2−(3)2dx⇒I=x+22√x2+4x−5−92log|(x+2)+√x2+4x−5|+C[∵∫√(x2−a2)dx=x2√x2−a2−a22log|x+√x2−a2|]

Integrate the function.
$\int \sqrt{x^{2} + 4 x - 5} d x .$