Question

integrate sec^2 x/4+tan x

Answer 1

the top is the derivative of the bottom

Answer 2

\[\int \frac{du}{u}\]

Answer 3

could you show me the steps? because i cant understand it

Answer 4

im not sure what you mean by steps. this is a basic antiderivative.

Answer 5

its of the from:\[\int \frac{1}{u}du\]
what would that integrate to?

Answer 6

ln u ?

Answer 7

yes; except u = 4+tan x

Answer 8

oh, and +c on the end :)

Answer 9

to dbl chk; take the derivative of ln(4+tan x) and see if you get that result

Answer 10

and how about this question ? integrate x^2+1/x^3+3x ?

Answer 11

same concept; notice that the top is almost the derivative of the bottom

Answer 12

what would ln(x^3+3x) derive to? and youll see whats missing

Answer 13

do i write integral sign 1/u x du/3 ?

Answer 14

that would work too ;)

Answer 15

it would be then 1/3 x du/u right ?

Answer 16

exactly

Answer 17

then i take the 1/3 out and it would be 1/u ?

Answer 18

youve got it, your like a pro by now

Answer 19

then i substitute it with x^3+3x ?

Answer 20

thanks ! you have helped me understand it better ! ;)

Answer 21

\[\frac{1}{3}\int \frac{1}{u}du\to\ \frac{1}{3}ln(u);\ u=x^3+3x\]