Question

Intergration problem

Answer 1

i have prblem with the "e"

Answer 2

if it was only x it would be easyier

Answer 3

You know what \(\dfrac{\mathrm d}{\mathrm dx}~e^{2x}\) is, right?

Answer 4

yes

Answer 5

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 \(5e^{2x}\)

Answer 6

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 \(2c = 5\)

Answer 7

i thought we have to take the antider wouldnt it be 5/2e^2x?

Answer 8

So that c is 5/2

Therefore integral of \(5e^{2x}\) is \(\dfrac{5e^{2x}}{2}\)

Answer 9

yes what do i do after ? for substition

Answer 10

substitution?

Well, you basically have \(\left.\dfrac{5}{2}e^{2x}~\right|_1^8 = \left(\dfrac{5}{2}e^{2(8)}\right)-\left(\dfrac{5}{2}e^{2(1)}\right)\)

Answer 11

ok

Answer 12

You know how to evaluate \(\displaystyle \int_1^8 5e^{2x}~\mathrm dx?\), right?

do same for other terms.

Answer 13

for 4/x i get 0 ?

Answer 14

i am right ?

Answer 15

-1+1 =0

Answer 16

\[\int\dfrac{4}{x}\mathrm~dx = 4\ln(8) - 4\ln(1)\]

Answer 17

idk i might be right , but my final solution is s/2e^14 + 196607.25

Answer 18

damn i am wrong

Answer 19

196607.25 isn't exact value?

Answer 20

k after simplity everything i get 5/2e^2x - 4lnx-3/4x^3/4(x)

Answer 21

k after simplity everything i get 5/2e^2x - 4lnx+3/4x^3/4(x

Answer 22

@geerky42

Answer 23

@ikram002p

Answer 24

@ganeshie8

Answer 25

@satellite73

Answer 26

@campbell_st

Answer 27

@satellite73

Answer 28

@triciaal

Answer 29

\[\int\limits \left(\sqrt[3]{x}+5 e^{2 x}-\frac{4}{x}\right) \, dx=\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}-4 \log (x) \]\[\frac{\partial \left(\frac{3 x^{4/3}}{4}+\frac{5 e^{2 x}}{2}-4 \log (x)\right)}{\partial x}=\sqrt[3]{x}+5 e^{2 x}-\frac{4}{x} \]

Answer 30

Sounds good