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)
+118673 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.
+118673 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.
+397 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
\(\displaystyle I_{n}=x\ln(x)^{n}-\int xn\ln(x)^{n-1}\frac{1}{x}dx \\ I_{n}=x\ln(x)^n-nI_{n-1}.\)
