Question

How do I integrate (4x^6+2x)^3(12x^5+1)dx by substitution?

Answer 1

\[\int\limits_{-1}^{0}(4x^6+2x)^3(12x^5+1)\]

Answer 2

\[=2\int\limits_{-1}^{0}\left( 2x^6+x \right)^3\left( 12x^5+1 \right)dx\]
put \[2x^6+x=t,\left( 12x^5+1 \right)dx=dt\]
find t when x=-1,and x=0
and integrate

Answer 3

surj the 2 out front should be 2^3

Answer 4

correct
thanks

Answer 5

So t = 2x^7/7 + x^2/2?

Answer 6

I'm stuck...

Answer 7

@surjithayer

Answer 8

How are you stuck? Please share what you already know and what you need to know. "Stuck" is too general a term.

Answer 9

Why can't I take a 2x out of the first set, why only a 2?

Answer 10

whenx=-1
\[t=2(-1)^6+(-1)=2-1=1\]
when x=0
\[t=2*0^6+0=0\]
\[I=2^3\int\limits_{1}^{0}t^6dt=?\]