Calculus UNIT510: What is U-SUB? -- Sage

#1a) integrate(x+1,x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, x^{2} + x$

#1b) show(integrate((x+1)^2,x)) show(expand((x+1)^3)/3)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} + x^{2} + x$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{3} \, x^{3} + x^{2} + x + \frac{1}{3}$

#1c) show(integrate((2*x+1)^2,x)) show(expand((2*x+1)^3)/3)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{4}{3} \, x^{3} + 2 \, x^{2} + x$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{8}{3} \, x^{3} + 4 \, x^{2} + 2 \, x + \frac{1}{3}$

#2) f(x)=sqrt(4*x-1) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{6} \, {\left(4 \, x - 1\right)}^{\frac{3}{2}}$

#3) f(x)=cos(7*x+5) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{7} \, \sin\left(7 \, x + 5\right)$

#4) f(x)=(x^2+2*x-3)^2*(x+1) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{6} \, {\left(x^{2} + 2 \, x - 3\right)}^{3}$

#5) f(x)=sin(x)^4*cos(x) integrate(f(x),x)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{5} \, \sin\left(x\right)^{5}$

#6) f(x)=tan(x)*sec(x)^2 show(integrate(f(x),x)) show(integrate(f(x),x,0,pi/4))

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, \tan\left(x\right)^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2}$

#7) f(x)=x^2*sqrt(x^3+1) show(integrate(f(x),x)) show(integrate(f(x),x,0,2))

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2}{9} \, {\left(x^{3} + 1\right)}^{\frac{3}{2}}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{52}{9}$

Calculus UNIT510: What is U-SUB?

2769 days ago by MATH4R2013