Question

How do you evaluate the integral using the substitution method? x/(4x^2 - 3)^0.4

Answer 1

u is the expression in the parenthesis of the denominator

Answer 2

so du=8x dx

Answer 3

then make an integral with u's in it

Answer 4

\[\int\frac{x}{(4x^2-3)^{0.4}}dx\]
say u=(4x^2-3) then du/dx=8x or xdx=du/8
the integral becomes: \[\int\frac{1}{8(u)^{0.4}}du\]

Answer 5

So you just put 8x in for u?

Answer 6

No, @imron07 set it up perfectly... solve the u integral... then put the x's back in after taking the integral by substituting u=4x^2-3 where ever u is.

Answer 7

you could see it as this\[\frac{1}{8}\int\limits_{}^{}u ^{-0.4}du\]use the power rule for integrals
after you are done, put the x's back in

Answer 8

Oh ok thank you guys!

Answer 9

No problem :)