anonymous
  • anonymous
FInd the indefinite integral using substitution. let u = 2x^2 + 3x + 9. (4x + 3)/ (2x^2 + 3x + 9)^(7/3)dx
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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
  • anonymous
need way more specific steps please
anonymous
  • anonymous
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 :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.