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y^{''}-2y^'-48y=0	y^{\prime\:\prime\:}-2y^{\prime\:}-48y=0
integral of 1/(9e^{-7x)+e^{7x}}	\int\:\frac{1}{9e^{-7x}+e^{7x}}dx
integral of 4cos^4(x)	\int\:4\cos^{4}(x)dx
derivative of (x/4 ^2)	\frac{d}{dx}((\frac{x}{4})^{2})
derivative of \sqrt[3]{(x-1/(x+1)})	\frac{d}{dx}(\sqrt[3]{\frac{x-1}{x+1}})
derivative of x^{3/5}sqrt(x^3+5)	\frac{d}{dx}(x^{\frac{3}{5}}\sqrt{x^{3}+5})
d/(dθ)(4-θ^2sin(θ))	\frac{d}{dθ}(4-θ^{2}\sin(θ))
(\partial)/(\partial x)(1/(2x+3y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2x+3y})
tangent of y=3-2x+4x^3,(-1,1)	tangent\:y=3-2x+4x^{3},(-1,1)
integral of sqrt(1+cos(x))	\int\:\sqrt{1+\cos(x)}dx
x^2(dy)/(dx)-2x^3e^{-1/x}=y	x^{2}\frac{dy}{dx}-2x^{3}e^{-\frac{1}{x}}=y
integral of sin(5x)sin(4x)	\int\:\sin(5x)\sin(4x)dx
slope ofintercept (4.1)(8.2)	slopeintercept\:(4.1)(8.2)
derivative of (sec(x+csc(x))/(csc(x)))	\frac{d}{dx}(\frac{\sec(x)+\csc(x)}{\csc(x)})
integral of cos(x)(tan(x)+sec(x))	\int\:\cos(x)(\tan(x)+\sec(x))dx
(\partial)/(\partial x)(-x^2y+4)	\frac{\partial\:}{\partial\:x}(-x^{2}y+4)
d/(d{x)}(sqrt(25-{x)^2-{y}^2-{z}^2})	\frac{d}{d{x}}(\sqrt{25-{x}^{2}-{y}^{2}-{z}^{2}})
(\partial)/(\partial x)(x^2ye^{x-z})	\frac{\partial\:}{\partial\:x}(x^{2}ye^{x-z})
inverse oflaplace 1/(1+s)*8/s	inverselaplace\:\frac{1}{1+s}\cdot\:\frac{8}{s}
integral of (e^u)/((1-e^u)^2)	\int\:\frac{e^{u}}{(1-e^{u})^{2}}du
(dy)/(dx)=y^2(4-e^x)	\frac{dy}{dx}=y^{2}(4-e^{x})
3y^{''}+5y^'-12y=0	3y^{\prime\:\prime\:}+5y^{\prime\:}-12y=0
d/(dy)(-2e^x+4xcos(y))	\frac{d}{dy}(-2e^{x}+4x\cos(y))
integral of 2x-8y	\int\:2x-8ydx
integral of (x^3-2x)/(x^2+3x+2)	\int\:\frac{x^{3}-2x}{x^{2}+3x+2}dx
integral of 1/(x^2sqrt(9x^2-1))	\int\:\frac{1}{x^{2}\sqrt{9x^{2}-1}}dx
integral of tan^3(11pix)	\int\:\tan^{3}(11πx)dx
derivative of 1/4 sin(2x)	\frac{d}{dx}(\frac{1}{4}\sin(2x))
integral of (x^{1/2})	\int\:(x^{\frac{1}{2}})dx
(dy)/(dx)+5y=20	\frac{dy}{dx}+5y=20
y^{''}+y=cot^2(x)	y^{\prime\:\prime\:}+y=\cot^{2}(x)
inverse oflaplace ((s+4))/((s^2-2s+4))	inverselaplace\:\frac{(s+4)}{(s^{2}-2s+4)}
(-16xy^2+3y)+(-16x^2y+3x)y^'=0	(-16xy^{2}+3y)+(-16x^{2}y+3x)y^{\prime\:}=0
tangent of x^2+xy+2y^2=18,(3,-3)	tangent\:x^{2}+xy+2y^{2}=18,(3,-3)
integral of x/(x^2+6x+13)	\int\:\frac{x}{x^{2}+6x+13}dx
integral of xe^{-x}sin(x)	\int\:xe^{-x}\sin(x)dx
limit as x approaches-infinity of x^4e^x	\lim\:_{x\to\:-\infty\:}(x^{4}e^{x})
derivative of 1-2e^{3x}	\frac{d}{dx}(1-2e^{3x})
derivative of f(x)=((3x^2)/(2x+4))^3,x=2	derivative\:f(x)=(\frac{3x^{2}}{2x+4})^{3},x=2
taylor 100x+0.01x^2	taylor\:100x+0.01x^{2}
derivative of 4(2-x^2^2)	\frac{d}{dx}(4(2-x^{2})^{2})
integral from 0 to ln(2) of 4(2-xe^x)	\int\:_{0}^{\ln(2)}4(2-xe^{x})dx
x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0	x^{2}\frac{d^{2}y}{dx^{2}}+x\frac{dy}{dx}+y=0
f(x)=e^{tan(x)}	f(x)=e^{\tan(x)}
derivative of 1-(x^2+y^2^{1/3})	\frac{d}{dx}(1-(x^{2}+y^{2})^{\frac{1}{3}})
integral of sqrt(4x-3-x^2)	\int\:\sqrt{4x-3-x^{2}}dx
(\partial)/(\partial x)(1/(xyz))	\frac{\partial\:}{\partial\:x}(\frac{1}{xyz})
slope of f(x)=-8x^2+7x	slope\:f(x)=-8x^{2}+7x
(x-8y)dx+4xdy=0	(x-8y)dx+4xdy=0
inverse oflaplace 1/((s-2)(s-1))	inverselaplace\:\frac{1}{(s-2)(s-1)}
derivative of sqrt(x^2+c)	\frac{d}{dx}(\sqrt{x^{2}+c})
derivative of (ln(x)/(x^7))	\frac{d}{dx}(\frac{\ln(x)}{x^{7}})
integral from 1 to 3 of 17r^3ln(r)	\int\:_{1}^{3}17r^{3}\ln(r)dr
y^'-(6y)/x =x^6e^x	y^{\prime\:}-\frac{6y}{x}=x^{6}e^{x}
d/(dy)(xysin(y)+xy^2sin(x)+1/x)	\frac{d}{dy}(xy\sin(y)+xy^{2}\sin(x)+\frac{1}{x})
limit as x approaches 3 of csc((pix)/4)	\lim\:_{x\to\:3}(\csc(\frac{πx}{4}))
integral of e^{-x}*cos(x)	\int\:e^{-x}\cdot\:\cos(x)dx
(xy^3+1)dx+x^2y^2dy=0	(xy^{3}+1)dx+x^{2}y^{2}dy=0
x(dy)/(dx)-x^2y=-x^2	x\frac{dy}{dx}-x^{2}y=-x^{2}
(y^'-e^{-t}+4)/y =-4,y(0)=3	\frac{y^{\prime\:}-e^{-t}+4}{y}=-4,y(0)=3
normal of(o,y)y= pi/2 ,(pi, pi/2)	normal\:of(o,y)y=\frac{π}{2},(π,\frac{π}{2})
derivative of arcsec(x^2+1)	\frac{d}{dx}(\arcsec(x^{2}+1))
limit as x approaches infinity of 3x^3(e^{-2/(x^3)}-1)	\lim\:_{x\to\:\infty\:}(3x^{3}(e^{-\frac{2}{x^{3}}}-1))
integral of pixcos(2x)	\int\:πx\cos(2x)dx
sum from n=1 to infinity of cos(1/(n^3))	\sum\:_{n=1}^{\infty\:}\cos(\frac{1}{n^{3}})
integral of 15x^2(x^3-1)^4	\int\:15x^{2}(x^{3}-1)^{4}dx
derivative of-15x^4+270x^2	derivative\:-15x^{4}+270x^{2}
derivative of 5e^{6x}	\frac{d}{dx}(5e^{6x})
integral of 8x^3e^{-x^2}	\int\:8x^{3}e^{-x^{2}}dx
y^'=y(xy^4+2)	y^{\prime\:}=y(xy^{4}+2)
limit as x approaches 9 of (x-9)^4	\lim\:_{x\to\:9}((x-9)^{4})
derivative of sin(x-x)	\frac{d}{dx}(\sin(x)-x)
derivative of ((3x^2e^x-4))/(x^2)	derivative\:\frac{(3x^{2}e^{x}-4)}{x^{2}}
integral of (t^3)/(sqrt(1-t^8))	\int\:\frac{t^{3}}{\sqrt{1-t^{8}}}dt
integral from 2 to 3 of e^{1-x}	\int\:_{2}^{3}e^{1-x}dx
(\partial)/(\partial y)(ln(y^2+1))	\frac{\partial\:}{\partial\:y}(\ln(y^{2}+1))
derivative of 4x^2-e^x	\frac{d}{dx}(4x^{2}-e^{x})
(dy)/(dx)=-1/(5xy)	\frac{dy}{dx}=-\frac{1}{5xy}
integral of ((ln(x))/x)^2	\int\:(\frac{\ln(x)}{x})^{2}dx
(\partial)/(\partial x)(300-20x^2+30y)	\frac{\partial\:}{\partial\:x}(300-20x^{2}+30y)
x(dy)/(dx)+1y=6y^2,y(1)=-1	x\frac{dy}{dx}+1y=6y^{2},y(1)=-1
sum from n=1 to infinity of 1/(2n+3)	\sum\:_{n=1}^{\infty\:}\frac{1}{2n+3}
tangent of x^2+6	tangent\:x^{2}+6
derivative of-49sin(7x)	\frac{d}{dx}(-49\sin(7x))
integral of 4sin(5x)+5sin(4x)	\int\:4\sin(5x)+5\sin(4x)dx
derivative of 2^x*ln(2)	derivative\:2^{x}\cdot\:\ln(2)
derivative of e^{-x}cos(1/2 x)	\frac{d}{dx}(e^{-x}\cos(\frac{1}{2}x))
limit as x approaches 0 of x^{8sin(x)}	\lim\:_{x\to\:0}(x^{8\sin(x)})
(xsqrt(1-x^2))^'	(x\sqrt{1-x^{2}})^{\prime\:}
integral of (sec^2(y))/(tan(y))	\int\:\frac{\sec^{2}(y)}{\tan(y)}dy
derivative of sin^2(tan(4x))	\frac{d}{dx}(\sin^{2}(\tan(4x)))
integral of tan(θ)sec(θ)	\int\:\tan(θ)\sec(θ)dθ
y^'=e^{4x+y}	y^{\prime\:}=e^{4x+y}
(\partial)/(\partial x)((-x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-x}{x^{2}+y^{2}})
limit as x approaches 2-of 1/((x-2)^2)	\lim\:_{x\to\:2-}(\frac{1}{(x-2)^{2}})
(dy)/(dx)=4x-5y	\frac{dy}{dx}=4x-5y
tangent of 2x^2+5x+1	tangent\:2x^{2}+5x+1
cos^2(t)y^'=1	\cos^{2}(t)y^{\prime\:}=1
integral of 1/(e^y)	\int\:\frac{1}{e^{y}}dy
integral from-5 to 5 of sqrt(25-x^2)	\int\:_{-5}^{5}\sqrt{25-x^{2}}dx

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