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laplacetransform te^{7t}	laplacetransform\:te^{7t}
(dy)/(dt)=3y+y^5,y(0)=1	\frac{dy}{dt}=3y+y^{5},y(0)=1
integral of (5.45)/((1+1.9t)^{0.9)}	\int\:\frac{5.45}{(1+1.9t)^{0.9}}dt
derivative of 1/8 ln(5x^2-2)	\frac{d}{dx}(\frac{1}{8}\ln(5x^{2}-2))
integral of xsec(3x^2+1)	\int\:x\sec(3x^{2}+1)dx
derivative of f(x)=sqrt(x)+\sqrt[4]{x}	derivative\:f(x)=\sqrt{x}+\sqrt[4]{x}
6(dy)/(dx)-2y=xy^4,y(0)=-2	6\frac{dy}{dx}-2y=xy^{4},y(0)=-2
((2y)/x+2x)+(2ln(x)-3)((dy)/(dx))=0	(\frac{2y}{x}+2x)+(2\ln(x)-3)(\frac{dy}{dx})=0
derivative of 1/(4^x)	derivative\:\frac{1}{4^{x}}
integral from 1/2 to 1 of 4/9 x(5-x^2)	\int\:_{\frac{1}{2}}^{1}\frac{4}{9}x(5-x^{2})dx
integral from 1 to t of 39x^{-3}	\int\:_{1}^{t}39x^{-3}dx
derivative of (xarctan(sqrt(x)))	\frac{d}{dx}((x)\arctan(\sqrt{x}))
integral from 36 to x of sqrt(1+9x)	\int\:_{36}^{x}\sqrt{1+9x}dx
derivative of (t-sqrt(t))/(t^{1/7)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{7}}}
derivative of (3x^2+1)/(2x)	derivative\:\frac{3x^{2}+1}{2x}
integral of cos(x)log_{10}(2)2^x	\int\:\cos(x)\log_{10}(2)2^{x}dx
d/(d{x)}({x}sin({y}-{z}))	\frac{d}{d{x}}({x}\sin({y}-{z}))
integral of (42)/(1-cos(7x))	\int\:\frac{42}{1-\cos(7x)}dx
tangent of f(x)=15x^3-10x^2+1,(1,6)	tangent\:f(x)=15x^{3}-10x^{2}+1,(1,6)
integral from b to 1 of 5ln(x)	\int\:_{b}^{1}5\ln(x)dx
y^{''}-y/4 =0	y^{\prime\:\prime\:}-\frac{y}{4}=0
derivative of 4/(16x^2+1)	\frac{d}{dx}(\frac{4}{16x^{2}+1})
(\partial)/(\partial x)(e^{xy})	\frac{\partial\:}{\partial\:x}(e^{xy})
derivative of y=((3x^2)/(2x+4))^3	derivative\:y=(\frac{3x^{2}}{2x+4})^{3}
inverse oflaplace 5/(s(s^2+5^2))	inverselaplace\:\frac{5}{s(s^{2}+5^{2})}
derivative of (y-c^2)	\frac{d}{dx}((y-c)^{2})
integral of cos^4(5x+4)	\int\:\cos^{4}(5x+4)dx
laplacetransform f(t)=2(1-e^{-5t})	laplacetransform\:f(t)=2(1-e^{-5t})
derivative of ln^2(2*2^x)	\frac{d}{dx}(\ln^{2}(2)\cdot\:2^{x})
derivative of y=ln(x-4)	derivative\:y=\ln(x-4)
integral of pi(9/(x^2+9))^2	\int\:π(\frac{9}{x^{2}+9})^{2}dx
4sqrt(xy)(dy)/(dx)=1	4\sqrt{xy}\frac{dy}{dx}=1
laplacetransform-5e^{2t}	laplacetransform\:-5e^{2t}
((x-4)^2)^'	((x-4)^{2})^{\prime\:}
sum from n=1 to infinity of n!(x-1)^n	\sum\:_{n=1}^{\infty\:}n!(x-1)^{n}
integral from 1 to 4 of x^2-3x	\int\:_{1}^{4}x^{2}-3xdx
integral from 0 to 4 of x/(x^2-1)	\int\:_{0}^{4}\frac{x}{x^{2}-1}dx
(\partial)/(\partial x)(sqrt(3x+2y-3))	\frac{\partial\:}{\partial\:x}(\sqrt{3x+2y-3})
area y=x^2,y=3-x,(0,1.3)	area\:y=x^{2},y=3-x,(0,1.3)
derivative of f(x)=3x^2e^x+e^x(x^3+1)	derivative\:f(x)=3x^{2}e^{x}+e^{x}(x^{3}+1)
integral of-8/(x^2)	\int\:-\frac{8}{x^{2}}dx
y^'=18.2-0.7y	y^{\prime\:}=18.2-0.7y
y^'=1-(2y)/(100+2x),y(0)=20	y^{\prime\:}=1-\frac{2y}{100+2x},y(0)=20
t^2y^'+y=0	t^{2}y^{\prime\:}+y=0
limit as x approaches 4 of x	\lim\:_{x\to\:4}(x)
inverse oflaplace (s+3)/((s+3)^2+4)	inverselaplace\:\frac{s+3}{(s+3)^{2}+4}
derivative of 1/2 cos(x/2)	\frac{d}{dx}(\frac{1}{2}\cos(\frac{x}{2}))
y^'=y^2+y	y^{\prime\:}=y^{2}+y
derivative of (3x+2^6)	\frac{d}{dx}((3x+2)^{6})
integral from-7 to 7 of 1/x	\int\:_{-7}^{7}\frac{1}{x}dx
limit as x approaches 2 of 3ln(x-1)	\lim\:_{x\to\:2}(3\ln(x-1))
tangent of y= x/(sqrt(9+x^2)),(0,0)	tangent\:y=\frac{x}{\sqrt{9+x^{2}}},(0,0)
integral of 40sin((pix)/3)+50	\int\:40\sin(\frac{πx}{3})+50dx
integral of sqrt(3+x)*(x+1)^2	\int\:\sqrt{3+x}\cdot\:(x+1)^{2}dx
(\partial)/(\partial x)(x^{1/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}})
derivative of (-8x/(x^2+1))	\frac{d}{dx}(\frac{-8x}{x^{2}+1})
area y=3x^2ln(x),y=12ln(x)	area\:y=3x^{2}\ln(x),y=12\ln(x)
sum from n=1 to infinity of 7e^{-2n}	\sum\:_{n=1}^{\infty\:}7e^{-2n}
integral of (x^2+y^2)	\int\:(x^{2}+y^{2})dx
integral of sqrt(4)-x^2	\int\:\sqrt{4}-x^{2}dx
derivative of 0.81t^2	derivative\:0.81t^{2}
integral of xe^{11x}	\int\:xe^{11x}dx
derivative of f(x)=x^{-11}	derivative\:f(x)=x^{-11}
area 3cos(pix),12x^2-3,-0.5,0.5	area\:3\cos(πx),12x^{2}-3,-0.5,0.5
area x=y^2-1,x=7-y^2	area\:x=y^{2}-1,x=7-y^{2}
derivative of x^3 1/3	\frac{d}{dx}(x^{3}\frac{1}{3})
area x,3x,-x+4	area\:x,3x,-x+4
integral of (x^2-y^2)/((x^2+y^2)^2)	\int\:\frac{x^{2}-y^{2}}{(x^{2}+y^{2})^{2}}dy
derivative of e^{xy^2}	derivative\:e^{xy^{2}}
derivative of (2x)/(-x+2)	derivative\:\frac{2x}{-x+2}
integral of 1/(3^{2x)}	\int\:\frac{1}{3^{2x}}dx
derivative of-1/(2x^{3/2})	\frac{d}{dx}(-\frac{1}{2x^{\frac{3}{2}}})
limit as x approaches 0 of tan^x(2x)	\lim\:_{x\to\:0}(\tan^{x}(2x))
derivative of y=2x^2sqrt(25-x^2)	derivative\:y=2x^{2}\sqrt{25-x^{2}}
y^'=xy-y	y^{\prime\:}=xy-y
integral of (2x)/(x^2+2)	\int\:\frac{2x}{x^{2}+2}dx
derivative of f(x)= 3/4 x^8	derivative\:f(x)=\frac{3}{4}x^{8}
derivative of 3/(sin(2x))	derivative\:\frac{3}{\sin(2x)}
2y^{''}+5y^'-3y=0,y(0)=3,y^'(0)=19	2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0,y(0)=3,y^{\prime\:}(0)=19
derivative of f(x)= 7/(8t^4)	derivative\:f(x)=\frac{7}{8t^{4}}
tangent of f(x)=2x^3-x^2+2,\at x=1	tangent\:f(x)=2x^{3}-x^{2}+2,\at\:x=1
integral of ln(t)	\int\:\ln(t)dt
derivative of ln(2-3x)	\frac{d}{dx}(\ln(2-3x))
area 11x,x^2-12	area\:11x,x^{2}-12
slope of (-1,-1),(0,0)	slope\:(-1,-1),(0,0)
derivative of sin(x+pi/2)	derivative\:\sin(x+\frac{π}{2})
y^'=(y^2+2xy)/(x^2)	y^{\prime\:}=\frac{y^{2}+2xy}{x^{2}}
integral from 0 to pi/2 of 4cos^5(x)	\int\:_{0}^{\frac{π}{2}}4\cos^{5}(x)dx
3y^{''}-6y^'+3y=0	3y^{\prime\:\prime\:}-6y^{\prime\:}+3y=0
(\partial)/(\partial y)((2x^2y)/(3+x^2y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x^{2}y}{3+x^{2}y^{2}})
integral of (e^t)/(1+e^t)	\int\:\frac{e^{t}}{1+e^{t}}dt
sum from n=0 to infinity of (0.5)^n	\sum\:_{n=0}^{\infty\:}(0.5)^{n}
inverse oflaplace 1/(s^2+2s+5)	inverselaplace\:\frac{1}{s^{2}+2s+5}
d/(dt)(t*cos(t))	\frac{d}{dt}(t\cdot\:\cos(t))
derivative of f(x)= 5/(2x)	derivative\:f(x)=\frac{5}{2x}
integral of (2y-3y^4-y^3) 1/y	\int\:(2y-3y^{4}-y^{3})\frac{1}{y}dy
y^'+y+3cos(x)=0	y^{\prime\:}+y+3\cos(x)=0
(\partial)/(\partial x)(x^2+2ysin(x))	\frac{\partial\:}{\partial\:x}(x^{2}+2y\sin(x))
limit as x approaches 0.9 of 4x	\lim\:_{x\to\:0.9}(4x)
(1+x^2)dy-(1+4y^2)dx=0	(1+x^{2})dy-(1+4y^{2})dx=0

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