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Flag Integral Calculus> ∫(x+1)/(4+8x-5x^2)^1/2 plz solve this in ...
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∫(x+1)/(4+8x-5x^2)^1/2
plz solve this in short method

Faizan Alam , 6 Years ago
Grade 12th pass
anser 1 Answers
Aditya Gupta

Last Activity: 6 Years ago

the trick to solving the above integral by shortest method is as follows:
write the numerator as:
((-10x+8)-10)/(-10), the reason being that 4+8x-5x^2 when differentiated gives -10x+8
splitting the integral this way makes it exceedingly easy to solve the first integral, but in order to solve the second integral, simply complete the square in the denominator as 5((6/5)^2-(x-4/5)^2)
now simply take the 5 out as root5, and then substitute x-4/5=y, thence resorting to the standard result of 
integration of 1/root(a^2-x^2)dx=arcsin(x/a)
 

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