anonymous
  • anonymous
Intergration problem
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
i have prblem with the "e"
anonymous
  • anonymous
if it was only x it would be easyier

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geerky42
  • geerky42
You know what \(\dfrac{\mathrm d}{\mathrm dx}~e^{2x}\) is, right?
anonymous
  • anonymous
yes
geerky42
  • geerky42
To 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
  • geerky42
Since \(\dfrac{\mathrm d}{\mathrm dx}~e^{2x} = 2e^{2x}\), you have \(\dfrac{\mathrm d}{\mathrm dx}~c~e^{2x} = 2c~e^{2x}\). Here, we have \(2c = 5\)
anonymous
  • anonymous
i thought we have to take the antider wouldnt it be 5/2e^2x?
geerky42
  • geerky42
So that c is 5/2 Therefore integral of \(5e^{2x}\) is \(\dfrac{5e^{2x}}{2}\)
anonymous
  • anonymous
yes what do i do after ? for substition
geerky42
  • geerky42
substitution? Well, you basically have \(\left.\dfrac{5}{2}e^{2x}~\right|_1^8 = \left(\dfrac{5}{2}e^{2(8)}\right)-\left(\dfrac{5}{2}e^{2(1)}\right)\)
anonymous
  • anonymous
ok
geerky42
  • geerky42
You know how to evaluate \(\displaystyle \int_1^8 5e^{2x}~\mathrm dx?\), right? do same for other terms.
anonymous
  • anonymous
for 4/x i get 0 ?
anonymous
  • anonymous
i am right ?
anonymous
  • anonymous
-1+1 =0
geerky42
  • geerky42
\[\int\dfrac{4}{x}\mathrm~dx = 4\ln(8) - 4\ln(1)\]
anonymous
  • anonymous
idk i might be right , but my final solution is s/2e^14 + 196607.25
anonymous
  • anonymous
damn i am wrong
geerky42
  • geerky42
196607.25 isn't exact value?
anonymous
  • anonymous
k after simplity everything i get 5/2e^2x - 4lnx-3/4x^3/4(x)
anonymous
  • anonymous
k after simplity everything i get 5/2e^2x - 4lnx+3/4x^3/4(x
anonymous
  • anonymous
@geerky42
anonymous
  • anonymous
@ikram002p
anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
@campbell_st
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
@triciaal
anonymous
  • anonymous
\[\int\limits \left(\sqrt[3]{x}+5 e^{2 x}-\frac{4}{x}\right) \, dx=\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}-4 \log (x) \]\[\frac{\partial \left(\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}-4 \log (x)\right)}{\partial x}=\sqrt[3]{x}+5 e^{2 x}-\frac{4}{x} \]
anonymous
  • anonymous
Sounds good

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