Evaluate the given indefinite integral. \int \frac{3-5xe^{x}}{x}dx

sklicatias

sklicatias

Answered question

2021-11-21

Evaluate the given indefinite integral.
35xexxdx

Answer & Explanation

David Tyson

David Tyson

Beginner2021-11-22Added 19 answers

Step 1
The given integral is
35xexxdx
Step 2
Obtain the value of the given integral as shown below:
35xexxdx=3xdx5xexxdx
=31xdx5exdx
=3ln|x|5ex+C
Alfonso Miller

Alfonso Miller

Beginner2021-11-23Added 20 answers

Step 1: Split fraction.
3x+5xexxdx
Step 2: Use Sum Rule: f(x)+g(x)dx=f(x)dx+g(x)dx.
3xdx+5exdx
Step 3: Use Constant Factor Rule: cf(x)dx=cf(x)dx.
31xdx+5exdx
Step 4: The derivative of lnx is 1x.
3lnx+5exdx
Step 5: Use Constant Factor Rule: cf(x)dx=cf(x)dx.
3lnx5exdx
Step 6: The integral of ex is ex.
3lnx5ex
Step 7: Add constant.
3lnx5ex+C

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