How do you solve #\int \frac { 10x ^ { 3} - 5x } { \sqrt { x ^ { 4} - x ^ { 2} + 6} } d x#?

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Answer 1 · 2018-08-11T02:53:48

#5sqrt(x^4-x^2+6)+C#

You can see that the derivative of the denominator has the same powers that are in the denominator, so we'll do a u-sub.

#u=x^4-x^2+6#
#du=4x^3-2x dx#

#1/2du=2x^3-xdx#

#5/2du=10x^3-5xdx#

#therefore 5/2intu^(-1/2)du#

#5/2[2u^(1/2)]#

#5u^(1/2)#

substitute back:

#5sqrt(x^4-x^2+6)+C#