anonymous
  • anonymous
integrate sec^2 x/4+tan x
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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amistre64
  • amistre64
the top is the derivative of the bottom
amistre64
  • amistre64
\[\int \frac{du}{u}\]
anonymous
  • anonymous
could you show me the steps? because i cant understand it

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amistre64
  • amistre64
im not sure what you mean by steps. this is a basic antiderivative.
amistre64
  • amistre64
its of the from:\[\int \frac{1}{u}du\] what would that integrate to?
anonymous
  • anonymous
ln u ?
amistre64
  • amistre64
yes; except u = 4+tan x
amistre64
  • amistre64
oh, and +c on the end :)
amistre64
  • amistre64
to dbl chk; take the derivative of ln(4+tan x) and see if you get that result
anonymous
  • anonymous
and how about this question ? integrate x^2+1/x^3+3x ?
amistre64
  • amistre64
same concept; notice that the top is almost the derivative of the bottom
amistre64
  • amistre64
what would ln(x^3+3x) derive to? and youll see whats missing
anonymous
  • anonymous
do i write integral sign 1/u x du/3 ?
amistre64
  • amistre64
that would work too ;)
anonymous
  • anonymous
it would be then 1/3 x du/u right ?
amistre64
  • amistre64
exactly
anonymous
  • anonymous
then i take the 1/3 out and it would be 1/u ?
amistre64
  • amistre64
youve got it, your like a pro by now
anonymous
  • anonymous
then i substitute it with x^3+3x ?
anonymous
  • anonymous
thanks ! you have helped me understand it better ! ;)
amistre64
  • amistre64
\[\frac{1}{3}\int \frac{1}{u}du\to\ \frac{1}{3}ln(u);\ u=x^3+3x\]

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