Can someone please help me with integrals?

Question

Can someone explain to me how to do integrals?

Here is an example:

(integral sign)
6x + 9
---------
(x^2 +3x +11)^-1/2

Answer 1

This is an excellent website which allows you to input your question and works the answer out for you.

http://integrals.wolfram.com/index.jsp

And:

http://en.wikibooks.org/wiki/Solving_Integrals_by_Trigonometric_substitution:Basic_trigonometric_integrals

Answer 2

you can rewrite this as IS (means integral sign)

IS 3 (x+3) / (x^2+3x+11)^-1/2 or since1/ ^-1/2 =^1/2

3 (x+3) (x^2+3x+11)^1/2

if you put x^2+3x+11 = u (x+3) =du

and you have to solve the integral IS 3*u^1/2 du

recall that integral of u^n = u^(n+1)/(n+1) her n=0.5 n+1 = 1.5


you have Integral = (3/1.5 ) (x^2+3x+11) ^1.5


and (3/1.5 ) = 2 hence result 2 (x^2+3x+11) ^1.5

Answer 3

3(2x+3) is the differential coefficient of the denominator x^2+3x+11
sub x^2+3x+11=t
(2x+3)dx=dt
the integral=3dt/t^-1/2d
=3(t^3/2)/3/2
=2t^3/2+C
=2(x^2+3x+11)3/2+C