Determine the following indefinite integral. \int \frac{x^{5}-3}{x}dx

Idilwsiw2 2021-11-19 Answered
Determine the following indefinite integral.
x53xdx
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Expert Answer

Theirl1972
Answered 2021-11-20 Author has 22 answers
Step 1
We have to determine the indefinite integral:
x53xdx
Step 2
We can write x53x as x43x
So, x53xdx=(x43x)dx
=x4dx3xdx
=x553ln(|x|)+C
Therefore, x53xdx=x553ln(|x|)+C
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Jennifer Hill
Answered 2021-11-21 Author has 10 answers
Step 1: Simplify x53xx43x.
x43xdx
Step 2: Use Sum Rule: f(x)+g(x)dx=f(x)dx+g(x)dx.
x4dx3xdx
Step 3: Use Power Rule: xndx=xn+1n+1+C.
x553xdx
Step 4: Use Constant Factor Rule: cf(x)dx=ff(x)dx.
x5531xdx
Step 5: The derivative of lnx is 1x.
x553lnx
Step 6: Add constant.
x553lnx+C
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