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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Integrate the function $e^{2x+3}$

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Toolbox:
  • Method of substitution :
  • Given f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t).
  • Consider $I=\int f(x)dx.$
  • Put x=g(t) so that $\frac{dx}{dt}=g'(t).$
  • dx=g'(t)dt.
  • Thus $I=\int f(g(t).g'(t))dt.$
Given $I=\int e^{2x+3}dx$.
 
Let 2x+3=t.
 
$\;\;2dx=dt \Rightarrow dx=\frac{dt}{2}$.
 
Now substituting for x and dx we get,
 
$\int e^{2x+3}dx=\frac{1}{2}\int e^t.dt.$
 
On integrating we get,
 
$\;\;\frac{1}{2}e^t+c.$
 
Substituting for t we get,
 
$\;\;\;\int e^{2x+3}dx=\frac{1}{2}e^{(2x+3)}+c.$
 
Hence $\int e^{2x+3}dx=\frac{1}{2}e^{(2x+3)}+c.$
 
 
 

 

answered Jan 28, 2013 by sreemathi.v
 
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