Lab one

111 days ago by soccer7

var ('x') integrate(ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}x \log\left(x\right) - x
\newcommand{\Bold}[1]{\mathbf{#1}}x \log\left(x\right) - x
var ('x') integrate(x*ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, x^{2} \log\left(x\right) - \frac{1}{4} \, x^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, x^{2} \log\left(x\right) - \frac{1}{4} \, x^{2}
var ('x') integrate(x^2*ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} \log\left(x\right) - \frac{1}{9} \, x^{3}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} \log\left(x\right) - \frac{1}{9} \, x^{3}
var ('x') integrate(x^3*ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{4} \, x^{4} \log\left(x\right) - \frac{1}{16} \, x^{4}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{4} \, x^{4} \log\left(x\right) - \frac{1}{16} \, x^{4}
var ('x') integrate(x^7*ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{8} \, x^{8} \log\left(x\right) - \frac{1}{64} \, x^{8}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{8} \, x^{8} \log\left(x\right) - \frac{1}{64} \, x^{8}
var ('x n') assume (n>0) integrate(x^n*ln(x),x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x^{{\left(n + 1\right)}} \log\left(x\right)}{n + 1} - \frac{x^{n + 1}}{{\left(n + 1\right)}^{2}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x^{{\left(n + 1\right)}} \log\left(x\right)}{n + 1} - \frac{x^{n + 1}}{{\left(n + 1\right)}^{2}}
var ('x') integrate(x*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)} e^{x}
var ('x') integrate(x^2*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{2} - 2 \, x + 2\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{2} - 2 \, x + 2\right)} e^{x}
var ('x') integrate(x^3*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{3} - 3 \, x^{2} + 6 \, x - 6\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{3} - 3 \, x^{2} + 6 \, x - 6\right)} e^{x}
var ('x') integrate(x^4*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right)} e^{x}
var ('x') integrate(x^5*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{5} - 5 \, x^{4} + 20 \, x^{3} - 60 \, x^{2} + 120 \, x - 120\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{5} - 5 \, x^{4} + 20 \, x^{3} - 60 \, x^{2} + 120 \, x - 120\right)} e^{x}
var ('x') integrate(x^6*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right)} e^{x}
var ('x n') integrate(x^6*e^x ,x) 
        
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{6} - 6 \, x^{5} + 30 \, x^{4} - 120 \, x^{3} + 360 \, x^{2} - 720 \, x + 720\right)} e^{x}