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)

Guest Jan 26, 2021

#1**+1 **

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.

Come back here with your answer.

Melody Jan 27, 2021

#2**+1 **

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.

Melody Jan 27, 2021

#7**+2 **

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

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

Tiggsy Jan 28, 2021