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laplacetransform {cos(t)}	laplacetransform\:\left\{\cos(t)\right\}
f(t)=cos(8t)	f(t)=\cos(8t)
derivative of f(x)=x^3-3x+4	derivative\:f(x)=x^{3}-3x+4
y^{''}+6y^'+5y=2x	y^{\prime\:\prime\:}+6y^{\prime\:}+5y=2x
tangent of f(x)=3x^{1/2}+x^{3/2},\at x=16	tangent\:f(x)=3x^{\frac{1}{2}}+x^{\frac{3}{2}},\at\:x=16
integral of 2/(x(ln(x))^2)	\int\:\frac{2}{x(\ln(x))^{2}}dx
derivative of (x^2)/((2+x))	derivative\:\frac{x^{2}}{(2+x)}
y^{''}-8y^'-17y=0	y^{\prime\:\prime\:}-8y^{\prime\:}-17y=0
derivative of 3x^2y-2x^2y^2+3y	\frac{d}{dx}(3x^{2}y-2x^{2}y^{2}+3y)
integral from 0 to pi/4 of 2tan^5(x)	\int\:_{0}^{\frac{π}{4}}2\tan^{5}(x)dx
taylor x^2-2x+42	taylor\:x^{2}-2x+42
area sqrt(1/7 x),7x^2	area\:\sqrt{\frac{1}{7}x},7x^{2}
limit as x approaches infinity of (x^2-1)e^{-x^2}	\lim\:_{x\to\:\infty\:}((x^{2}-1)e^{-x^{2}})
integral of-xcos(x+pi/3)	\int\:-x\cos(x+\frac{π}{3})dx
integral of (2sqrt(x)-3\sqrt[4]{x})	\int\:(2\sqrt{x}-3\sqrt[4]{x})dx
integral of x^2e^{-2x^3}	\int\:x^{2}e^{-2x^{3}}dx
integral of sqrt(2[1-cos^2(\sqrt{2x))]}	\int\:\sqrt{2[1-\cos^{2}(\sqrt{2x})]}dx
integral from-1 to 1 of pi(2-2x^2)^2	\int\:_{-1}^{1}π(2-2x^{2})^{2}dx
y^{''}+2y^'-15y=4e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}-15y=4e^{-t}
(\partial)/(\partial y)(x^2-y)	\frac{\partial\:}{\partial\:y}(x^{2}-y)
2y^{''}+5y^'-3y=0	2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0
(\partial)/(\partial y)(2xy+z^2)	\frac{\partial\:}{\partial\:y}(2xy+z^{2})
(\partial)/(\partial x)(3xln(y)+yln(z)-2x)	\frac{\partial\:}{\partial\:x}(3x\ln(y)+y\ln(z)-2x)
integral of sqrt(x)(x+1/x)	\int\:\sqrt{x}(x+\frac{1}{x})dx
integral of x^2	\int\:x^{2}dx
limit as x approaches 0+of (2x)/(\|x\|)	\lim\:_{x\to\:0+}(\frac{2x}{\left\|x\right\|})
derivative of sqrt(x)(x^2-1)	\frac{d}{dx}(\sqrt{x}(x^{2}-1))
derivative of sqrt((x+2^2*(x^2)/2))	\frac{d}{dx}(\sqrt{(x+2)^{2}\cdot\:\frac{x^{2}}{2}})
derivative of (e^x/(5x^3))	\frac{d}{dx}(\frac{e^{x}}{5x^{3}})
tangent of f(x)=(1+5x)^{12},(0,1)	tangent\:f(x)=(1+5x)^{12},(0,1)
10y^'=10*9.81-5y	10y^{\prime\:}=10\cdot\:9.81-5y
tangent of y= 1/(x-1),\at x=6	tangent\:y=\frac{1}{x-1},\at\:x=6
y^{''}-4y^'+3y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0
derivative of-10sin(2x+10)	\frac{d}{dx}(-10\sin(2x+10))
y^{''}+25y=-20sin(5t)	y^{\prime\:\prime\:}+25y=-20\sin(5t)
derivative of 3cos(3x+1)	\frac{d}{dx}(3\cos(3x+1))
limit as x approaches 81 of ((\sqrt[4]{x}-3))/(x-81)	\lim\:_{x\to\:81}(\frac{(\sqrt[4]{x}-3)}{x-81})
(\partial)/(\partial u)(b((((Nu))/(V(u)))^{(2/3)}))	\frac{\partial\:}{\partial\:u}(b((\frac{(Nu)}{V(u)})^{(\frac{2}{3})}))
integral from 1 to infinity of 1/(x^2)	\int\:_{1}^{\infty\:}\frac{1}{x^{2}}dx
taylor ln(x+1),2	taylor\:\ln(x+1),2
(\partial)/(\partial x)((x^2)/((y-x)^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{(y-x)^{2}})
sum from n=1 to infinity of 2/(n^8)	\sum\:_{n=1}^{\infty\:}\frac{2}{n^{8}}
integral of 8x^4	\int\:8x^{4}dx
integral of sqrt(x)sin^2(x^{3/2}-1)	\int\:\sqrt{x}\sin^{2}(x^{\frac{3}{2}}-1)dx
derivative of 7x^3-3x^2+3x-12	\frac{d}{dx}(7x^{3}-3x^{2}+3x-12)
(ln(x+1))^2	(\ln(x+1))^{2}
derivative of (x^2/(1+x^2))	\frac{d}{dx}(\frac{x^{2}}{1+x^{2}})
integral of (2x^3)/(x^4+5)	\int\:\frac{2x^{3}}{x^{4}+5}dx
derivative of acos^2(x)+bx	derivative\:a\cos^{2}(x)+bx
integral of (sin(x)-4cos(x))	\int\:(\sin(x)-4\cos(x))dx
integral of (x+3)/((x-1)(x^2+1))	\int\:\frac{x+3}{(x-1)(x^{2}+1)}dx
derivative of ln(sqrt(3x+4))	\frac{d}{dx}(\ln(\sqrt{3x+4}))
limit as x approaches 6+of xsqrt(6-x)	\lim\:_{x\to\:6+}(x\sqrt{6-x})
limit as x approaches 0 of (x)sin(1/x)	\lim\:_{x\to\:0}((x)\sin(\frac{1}{x}))
limit as x approaches-7 of (x^2-3)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-3}{7-x})
derivative of 8(x-1/x)^3	derivative\:8(x-\frac{1}{x})^{3}
integral of 6x^2-8x+3	\int\:6x^{2}-8x+3dx
derivative of x^3(3-x)^4	derivative\:x^{3}(3-x)^{4}
integral of sqrt(1+(1/(x^{1/3)))^2}	\int\:\sqrt{1+(\frac{1}{x^{\frac{1}{3}}})^{2}}dx
derivative of sqrt(100+x^2)	\frac{d}{dx}(\sqrt{100+x^{2}})
derivative of y=x6^x	derivative\:y=x6^{x}
x(x+y)((dy)/(dx))+y(3x+y)=0	x(x+y)(\frac{dy}{dx})+y(3x+y)=0
derivative of y=ln(arctan(4x))	derivative\:y=\ln(\arctan(4x))
integral from 1 to 3 of 5r^3ln(r)	\int\:_{1}^{3}5r^{3}\ln(r)dr
y^{''}-y^'-2y=2e^{-t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=2e^{-t}
integral of tan^3(x)sec^{1/2}(x)	\int\:\tan^{3}(x)\sec^{\frac{1}{2}}(x)dx
limit as x approaches 0 of 1/(e^x)	\lim\:_{x\to\:0}(\frac{1}{e^{x}})
limit as x approaches 6 of x/(x^2-36)	\lim\:_{x\to\:6}(\frac{x}{x^{2}-36})
(dx)/(dt)+x=-e^t	\frac{dx}{dt}+x=-e^{t}
derivative of (3t^2-t+a^2^{101})	\frac{d}{dx}((3t^{2}-t+a^{2})^{101})
limit as x approaches+3+of 7/(x-3)	\lim\:_{x\to\:+3+}(\frac{7}{x-3})
(\partial)/(\partial x)(-2y)	\frac{\partial\:}{\partial\:x}(-2y)
integral of (sqrt(a^2+x^2))/(x^4)	\int\:\frac{\sqrt{a^{2}+x^{2}}}{x^{4}}dx
integral of (7x^2)/((x+1)(x^2+1))	\int\:\frac{7x^{2}}{(x+1)(x^{2}+1)}dx
derivative of sin(x^2)	\frac{d}{dx}(\sin(x^{2}))
(\partial)/(\partial y)(arcsin(x/y))	\frac{\partial\:}{\partial\:y}(\arcsin(\frac{x}{y}))
derivative of \sqrt[5]{2-x^2}	\frac{d}{dx}(\sqrt[5]{2-x^{2}})
taylor e^{x^2+x}	taylor\:e^{x^{2}+x}
derivative of sqrt(y^2-x)	\frac{d}{dx}(\sqrt{y^{2}-x})
simplify e^{ln(sin(x^2))}sqrt(2x+1)	simplify\:e^{\ln(\sin(x^{2}))}\sqrt{2x+1}
limit as x approaches 0 of (ln(x+1))/x	\lim\:_{x\to\:0}(\frac{\ln(x+1)}{x})
integral of cos^2(10x)	\int\:\cos^{2}(10x)dx
derivative of (x^4+2^{cos(x)})	\frac{d}{dx}((x^{4}+2)^{\cos(x)})
limit as x approaches-3 of x^3	\lim\:_{x\to\:-3}(x^{3})
y^{''}+9y=2sec(3t)	y^{\prime\:\prime\:}+9y=2\sec(3t)
derivative of i/x	\frac{d}{dx}(\frac{i}{x})
derivative of 6(sec(x+tan(x))^{3/2})	\frac{d}{dx}(6(\sec(x)+\tan(x))^{\frac{3}{2}})
(\partial)/(\partial x)(x^5sin(y))	\frac{\partial\:}{\partial\:x}(x^{5}\sin(y))
integral of xcos(7x^2)	\int\:x\cos(7x^{2})dx
derivative of x/x	\frac{d}{dx}(\frac{x}{x})
integral from 0 to 1 of sqrt(3+9x^2)	\int\:_{0}^{1}\sqrt{3+9x^{2}}dx
derivative of (e^x/(9x))	\frac{d}{dx}(\frac{e^{x}}{9x})
integral from 0 to 1 of (2x-3)(5x+1)	\int\:_{0}^{1}(2x-3)(5x+1)dx
integral of 1/2 sin(x)	\int\:\frac{1}{2}\sin(x)dx
limit as x approaches 8+of log_{5}(x-8)	\lim\:_{x\to\:8+}(\log_{5}(x-8))
integral from 0 to 2 of x/(x+1)	\int\:_{0}^{2}\frac{x}{x+1}dx
derivative of log_{5}((6x^3+4/(2x^3-3)))	\frac{d}{dx}(\log_{5}(\frac{6x^{3}+4}{2x^{3}-3}))
slope ofintercept (4,-3),(12,0)	slopeintercept\:(4,-3),(12,0)
integral from 2 to 3 of (25)/(sqrt(3-x))	\int\:_{2}^{3}\frac{25}{\sqrt{3-x}}dx
integral of (3ln(x))/(x^3)	\int\:\frac{3\ln(x)}{x^{3}}dx

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