FInd the indefinite integral using substitution. let u = 2x^2 + 3x + 9.
(4x + 3)/ (2x^2 + 3x + 9)^(7/3)dx

Question

anonymous · Answer

Substitute u into the equation and then solve for dx by taking the derivative of u. This will make the integration fall in place nicely.

anonymous · Answer

need way more specific steps please

anonymous · Answer

Alright. so if $$u=2x^2+3x+9$$ then we can replace $$2x^2+3x+9$$ with u in the equation being integrated to get the integral of (4x+3)/(u)^(7/3) dx Now we have to get rid of the dx somehow since we now have a u in out integral so we take the derivative of u so $$du/dx=4x+3$$ This can then be solved for dx which gives dx=du/(4x+3) Now if we plug dx into our integral equation we get (4x+3)/(u)^(7/3) *du/(4x+3) the * represents multiplication. Next, realize the (4x+3) quantities cancel leaving 1/(u)^(7/3) du which can be rewritten as u^(-7/3)du From here you simply integrate with respect to x and then at the end substitute the u back in from the beginning. Hope this is clear enough :)