how would i go about intergrating
(2x+1)^2

Question

how would i go about intergrating 
(2x+1)^2

anonymous · Answer

First rewrite to 4x^2+4x+1. then integrate each term seperately.

amistre64 · Answer

another way is to say that u = 2x+1; du = 2 dx

dx = du/2

     u^2
{S} ---- du ; maybe?
       2

anonymous · Answer

what if i had to integrate sqrt(2x+1)

anonymous · Answer

but i could not use substituiton

amistre64 · Answer

why would you not be able to use substitution?  thats like saying, I want you to move 3 feet to your left; but you have to move right to get there .....

anonymous · Answer

is there a way, to find the anti derivative, without using substitution for a problem like this

amistre64 · Answer

sure; its called being creative and reinventing the wheel ...

amistre64 · Answer

looking ahead to see what you can do to derive an unknown function down to it with the knowledge yo have of derivatives ...

anonymous · Answer

the reason i ask this, is beacuse no where in the current chapter i am studying, does it meantion anything about substitution.

anonymous · Answer

The substitiuion is discussed in a later chapter

amistre64 · Answer

then focus on predicting the future :)

()^1/2 comes from ()^3/2

2()^3/2
------  is where it comes from; now anticipate the chain rule
    3

2x+1 pops out of there and sticks a 2 to it ... place something in the equation to catch it and get rid of it ... like 1/2

2(2x+1)^(3/2)                              (2x+1)^(3/2)
------------- which reduces to  ------------- maybe?
          6                                                 3

anonymous · Answer

can you help me integrate (x cos (x^2))-sin(x^2))/(x^2)

amistre64 · Answer

you seem to either have an extra ) or not enough (

amistre64 · Answer

either way, I gotta head to class :)  good luck