(e^2x+1)/e^x dx integrate by substitution method
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intg (e^2x+1)/e^x dx
Let t = e^x
==> dt = e^x dx = tdx ==> dx = dt/t
==> intg (e^2x+ 1)/e^x) dx = intg (t^2 + 1)/t * dt/t
= intg (t^2 +...
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To integrate (e^2x+1)/e^x
Solution:
(e^2x+1)/e^x = e^2x/e^x +1/e^x= e^x + e^(-x)
Int [(e^2x +1)/e^x ]dx = Int (e^x+e^-x)dx = e^x+e^(-x)/(-1) = e^x-e^-x + C, where C is the constant of integration.Substitution method:
Substitution method:
Substitute e^x = t. Then, e^x dx = dt. Or dx = dt/t.
Int [e^2x+1)/e^x]dx = Int{(t^2+1)/t}dt/t = Int(1+1/t^2)dt
=Int1*dt + Int(1/t^2) dt
= t + t^(-2+1)/(-2+1)
= t - t^(-1)
= e^x -e^(-x) + Constant
= t
(e^2x+1)/e^x = (t^2+1)/t
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