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# Calc Help

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Im having some difficulty with these question, I do kinda know where to start but Im just missing something

1. For positive integer n, represent it in terms of n, x, and I(n-1) $$I(n) = \int \log(x)^n \, dx.$$

2. Compute $$\int 4x^3e^{x^2}\,dx$$

3. Compute $$\int_0^{10} xg''(x)\,dx$$

using this the values g(x): (0,20), (2,10), (4,5), (6,19), (8,17), (10,2)

g'(x): (0,-9), (2,-2), (4,9), (6,10), (8,0), (10,-4)

Jan 26, 2021

#1
+112523
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Please just put one question per post.

Question 2

let

$$u=2x^2 \quad and \quad v'=2xe^{x^2}$$

Now  use integration by parts to solve.

Jan 27, 2021
#4
+1

ok,  i will remeber that for next time.

the answer to 2) is 2x^(2)(e^x^2) - (e^x^2) + C

and the answer to 3) is -22

Guest Jan 27, 2021
#6
+112523
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Good work and thanks for responding.

We always want feedback.

I got the same answers as you.

Although my personal preference is to factorize the Q2 answer.

Melody  Jan 27, 2021
#2
+112523
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question 3

let

$$u=x \qquad and \qquad v'=g''(x)$$

And again use integration by parts

Question 1:

I do not understand the question.

Jan 27, 2021
#3
+31703
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I suspect question 1 is meant to look like the following (also integration by parts):

Alan  Jan 27, 2021
#5
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I had the idea to turn Log(x)^n into n * log(x), I also noticed you use I(n-2) as a part of the equation which I think is not belonging in the question

Guest Jan 27, 2021
#7
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Here's a slightly different parts routine

Let

$$\displaystyle I_{n}=\int1.\ln(x)^{n}dx\\ \text{and let } u=\ln(x)^{n}, \quad dv = 1.dx$$

Then

$$\displaystyle \frac{du}{dx}=n.\ln(x)^{n-1}\frac{1}{x},\quad v = x$$

so

$$\displaystyle I_{n}=x\ln(x)^{n}-\int xn\ln(x)^{n-1}\frac{1}{x}dx \\ I_{n}=x\ln(x)^n-nI_{n-1}.$$

Jan 28, 2021
#8
+31703
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Much neater Tiggsy.

Alan  Jan 28, 2021