Question

integration of (e^(2logx))×(x^(-3))dx

Answer 1

e^(2logx)=x²
so,
x²•(x^(-3))=x^(-1)=1/x
now , integration of 1/x=logx

Answer 2

$\displaystyle \sf{ \int {e}^{2logx} \: {x}^{ - 3} \: dx = log \: x + c}$

Given :

The integral

$\displaystyle \sf{ \int {e}^{2logx} \: {x}^{ - 3} \: dx }$

To find :

To integrate

Solution :

Step 1 of 2 :

Write down the given Integral

The given Integral is

$\displaystyle \sf{ \int {e}^{2logx} \: {x}^{ - 3} \: dx }$

Step 2 of 2 :

Integrate the integral

$\displaystyle \sf{ \int {e}^{2logx} \: {x}^{ - 3} \: dx }$

$\displaystyle \sf{ = \int {e}^{log {x}^{2} } \: {x}^{ - 3} \: dx }$

$\displaystyle \sf{ = \int {x}^{2} . \: {x}^{ - 3} \: dx }$

$\displaystyle \sf{ = \int {x}^{2 - 3} \: dx }$

$\displaystyle \sf{ = \int {x}^{ - 1} \: dx }$

$\displaystyle \sf{ = \int \frac{1}{x} \: dx }$

$\displaystyle \sf{ = log \: x + c }$

Where c is integration constant

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