Solve the indefinite integral. \int_{2}^{3}\frac{x^{3}-2x}{x-1}dx

sklicatias

sklicatias

Answered question

2021-11-20

Solve the indefinite integral.
23x32xx1dx

Answer & Explanation

Sue Leahy

Sue Leahy

Beginner2021-11-21Added 13 answers

Step 1
Some integration formulas:
xndx=xn+1n+1+C
1xdx=logx+C
Given integral is I=23x32xx1dx
Let us assume:
x−1=u
dx=du
Transformed integral is given as:
I=12(u+1)32(u+1)udu
=12(u2+3u1u+1)du
Step 2
Next, integrate terms in pervious steps to get simplified form:
I=[u33+3u22ln(u)+u]12
=[83+6ln(2)+21332+ln(1)1]
=[73+732ln(2)]
=476ln(2)
=7.14
Hence 23x32xx1dx=7.14
John Twitchell

John Twitchell

Beginner2021-11-22Added 19 answers

Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
abf(x)dx=F(x)ab=F(b)F(a)
Step 2: In this case, f(x)=x32xx1. Find its integral.
x33+x22xln(x1)23
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(3)−F(2):
(333+3223ln(31))(233+2222ln(21))
Step 4: Simplify.
476ln2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?