Posted by Ashley on Friday, February 22, 2013 at 3:29pm.
Find the integral of
x^2 divided by the square root of (2xx^2) dx

Calculus  Reiny, Friday, February 22, 2013 at 4:24pm
x^2/(2x  x^2)
= x/2  1
so int(x^2/(2x  x^2) dx
= int (x/2  1 ) dx
= (1/4)x^2  x + c

Calculus  Steve, Friday, February 22, 2013 at 4:58pm
eh? That's some fancy division there.
I get
2/(2x)  1
so the integral is
2 ln(2x)  x
or some equivalent

Calculus  Steve, Friday, February 22, 2013 at 5:14pm
Oops. I missed that pesky square root.
Let u = x1 and we have
integral (u+1)^2/√(1u^2) du
Now if u = sinθ
du = cosθ dθ
and we have integral of
(1+sinθ)^2 dθ
3/2 θ  1/4 sin2θ  2cosθ
= 3/2 arcsin(u)  1/2 u√(1u^2)  2√(1u^2)
= 3/2 arcsin(x1)  1/2 (x1)√(2xx^2)  2√(2xx^2)
= 1/2 (3arcsin(x1)  (x+3)√(2xx^2))

Calculus  Reiny, Friday, February 22, 2013 at 5:30pm
Ohhh my!!!
Mea Culpa!!!
That is embarrassing! What was I thinking??
Answer This Question
Related Questions
 Calculus  Find the exact area of the region enclosed by the square root of (x...
 Math  Rationalize the denominator. Assume that all expressions under radicals ...
 calculus  how do you solve the integral of 1/[(square root of x)(lnx)] from 2 ...
 Pre Algebra  State if each number is Rational,Irrational,or not a real number...
 Calculus  Which of the following integrals cannot be evaluated using a simple ...
 Calculus  Which of the following integrals cannot be evaluated using a simple ...
 Algebra  Simplify: 3 squared divided by the square root of 80. Multiple choices...
 math, calculus  find the derivative of the function y= integral from square ...
 Algebra  Express the following in simplest radical form. All variables ...
 Maths Calculus Derivative Integral  Urgent Please  Use 2nd Fundamental Theorem...
More Related Questions