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anonymous
 one year ago
Intergration problem
anonymous
 one year ago
Intergration problem

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i have prblem with the "e"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if it was only x it would be easyier

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0You know what \(\dfrac{\mathrm d}{\mathrm dx}~e^{2x}\) is, right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0To find integral of \(5e^{2x}\), you want to look for value \(c\) in \(c~e^{2x}\) such that taking derivaitve it would give you \(5e^{2x}\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0Since \(\dfrac{\mathrm d}{\mathrm dx}~e^{2x} = 2e^{2x}\), you have \(\dfrac{\mathrm d}{\mathrm dx}~c~e^{2x} = 2c~e^{2x}\). Here, we have \(2c = 5\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought we have to take the antider wouldnt it be 5/2e^2x?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0So that c is 5/2 Therefore integral of \(5e^{2x}\) is \(\dfrac{5e^{2x}}{2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes what do i do after ? for substition

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0substitution? Well, you basically have \(\left.\dfrac{5}{2}e^{2x}~\right_1^8 = \left(\dfrac{5}{2}e^{2(8)}\right)\left(\dfrac{5}{2}e^{2(1)}\right)\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0You know how to evaluate \(\displaystyle \int_1^8 5e^{2x}~\mathrm dx?\), right? do same for other terms.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\dfrac{4}{x}\mathrm~dx = 4\ln(8)  4\ln(1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0idk i might be right , but my final solution is s/2e^14 + 196607.25

geerky42
 one year ago
Best ResponseYou've already chosen the best response.0196607.25 isn't exact value?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0k after simplity everything i get 5/2e^2x  4lnx3/4x^3/4(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0k after simplity everything i get 5/2e^2x  4lnx+3/4x^3/4(x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits \left(\sqrt[3]{x}+5 e^{2 x}\frac{4}{x}\right) \, dx=\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}4 \log (x) \]\[\frac{\partial \left(\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}4 \log (x)\right)}{\partial x}=\sqrt[3]{x}+5 e^{2 x}\frac{4}{x} \]
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