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∫(x+1)/(4+8x-5x^2)^1/2 plz solve this in short method

∫(x+1)/(4+8x-5x^2)^1/2
plz solve this in short method

Grade:12th pass

1 Answers

Aditya Gupta
2080 Points
3 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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