Question

can someone please show me how to find the integral of y^2/25+y^2

Answer 1

do you mean y^2/(25+y^2)? or (y^2/25) + y^2?

Answer 2

the first one

Answer 3

ok, did you get past the long division at the beginning which gives you 1- (25/y^2+25)?

Answer 4

why do i have to use long division

Answer 5

i would, you have same degree of y in numerator & denominator.

Answer 6

oh yes you are correct

Answer 7

long division gives 1 - (25/(y^2+25))...integral of 1 = y, integral of -25/(y^2+25) = -5arctan(y/5).....so the solution is y-5arctan(y/5)...

Answer 8

can you please explain how you got the integral of -25/(y^2+25)

Answer 9

25 * (1/(Y^2 + 5^2))--once you see the trig integrals enough, they just become easy to recognize.

Answer 10

integral of 1/(x^2 + a^2) = (1/a)arctan(x/a)

Answer 11

okay thank you