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Popular Calculus Problems

(y+4)y^'=y(2x+4)	(y+4)y^{\prime\:}=y(2x+4)
longdivision (3x-1)/(2x+1)	longdivision\:\frac{3x-1}{2x+1}
tangent of sqrt(x)(1.1)	tangent\:\sqrt{x}(1.1)
(\partial)/(\partial x)(2x-3y)	\frac{\partial\:}{\partial\:x}(2x-3y)
integral of 4/(6+4x)	\int\:\frac{4}{6+4x}dx
integral from-r to r of (sqrt(r^2-x^2))	\int\:_{-r}^{r}(\sqrt{r^{2}-x^{2}})dx
y^'=0.21-y/(1700)	y^{\prime\:}=0.21-\frac{y}{1700}
integral from-5 to 0 of xsqrt(4-x)	\int\:_{-5}^{0}x\sqrt{4-x}dx
(d^2)/(dx^2)(ln(sqrt(x^2+y^2)))	\frac{d^{2}}{dx^{2}}(\ln(\sqrt{x^{2}+y^{2}}))
(\partial)/(\partial x)(ln(x+z)-yz)	\frac{\partial\:}{\partial\:x}(\ln(x+z)-yz)
d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0	\frac{d}{dt}(\frac{dx}{dt})+\frac{d}{dt}(6x)+10x=0
integral of x^2cos(kx)	\int\:x^{2}\cos(kx)dx
integral of 2^{2x+1}	\int\:2^{2x+1}dx
integral of 1/(ax+bx^2)	\int\:\frac{1}{ax+bx^{2}}dx
limit as x approaches-1 of (x^2-1)/(x+1)	\lim\:_{x\to\:-1}(\frac{x^{2}-1}{x+1})
(d^5)/(dx^5)(1/(x^2))	\frac{d^{5}}{dx^{5}}(\frac{1}{x^{2}})
integral of 1/(s^3-1)	\int\:\frac{1}{s^{3}-1}ds
derivative of xarctan(2x-1/4 ln(1+4x^2))	\frac{d}{dx}(x\arctan(2x)-\frac{1}{4}\ln(1+4x^{2}))
tangent of 9x^{3/5}-2x^{6/7},\at x=3	tangent\:9x^{\frac{3}{5}}-2x^{\frac{6}{7}},\at\:x=3
tangent of f(x)=tan(x),((3pi)/4 ,-1)	tangent\:f(x)=\tan(x),(\frac{3π}{4},-1)
limit as x approaches 2pi of csc(x)	\lim\:_{x\to\:2π}(\csc(x))
derivative of sqrt(9-x^2)	derivative\:\sqrt{9-x^{2}}
(dy)/(dx)=sqrt(9y)*e^{x+9}	\frac{dy}{dx}=\sqrt{9y}\cdot\:e^{x+9}
y^{''}+2y^'=x^2+e^{-2x}	y^{\prime\:\prime\:}+2y^{\prime\:}=x^{2}+e^{-2x}
tangent of f(x)=sqrt(x),\at x=64.2	tangent\:f(x)=\sqrt{x},\at\:x=64.2
limit as x approaches 3 of sqrt(6x^2+2)	\lim\:_{x\to\:3}(\sqrt{6x^{2}+2})
integral of ((x+1))/(sqrt(x^2+2x-4))	\int\:\frac{(x+1)}{\sqrt{x^{2}+2x-4}}dx
integral from 1 to 100 of (25)/(x^3)	\int\:_{1}^{100}\frac{25}{x^{3}}dx
integral from 0 to x^3 of ye^{-y/x}	\int\:_{0}^{x^{3}}ye^{-\frac{y}{x}}dy
derivative of y=sin(tan(9x))	derivative\:y=\sin(\tan(9x))
derivative of (8x)/(7-tan(x))	derivative\:\frac{8x}{7-\tan(x)}
integral of 1/(sqrt(49-x^2))	\int\:\frac{1}{\sqrt{49-x^{2}}}dx
y^'=-ysin(2x)	y^{\prime\:}=-y\sin(2x)
integral of e^{-1/(2x)}	\int\:e^{-\frac{1}{2x}}dx
m(x)=x^3-x^2+1	m(x)=x^{3}-x^{2}+1
limit as x approaches 10.6 of ln(x^2-9)	\lim\:_{x\to\:10.6}(\ln(x^{2}-9))
integral of sin^{1/2}(x)	\int\:\sin^{\frac{1}{2}}(x)dx
integral of arctan(v)	\int\:\arctan(v)dv
integral of sqrt(x)+\sqrt[3]{x}	\int\:\sqrt{x}+\sqrt[3]{x}dx
integral of 2/(1-x)	\int\:\frac{2}{1-x}dx
y^'-y=x+1	y^{\prime\:}-y=x+1
(dr)/(ds)=0.05r	\frac{dr}{ds}=0.05r
limit as x approaches 0 of sin(1/x)*x	\lim\:_{x\to\:0}(\sin(\frac{1}{x})\cdot\:x)
integral of (cot(b)θ+tan(b)θ)^2	\int\:(\cot(b)θ+\tan(b)θ)^{2}dθ
sum from n=0 to infinity of (9n!)/(n^n)	\sum\:_{n=0}^{\infty\:}\frac{9n!}{n^{n}}
d/(dy)(1/(y^3+4y^2))	\frac{d}{dy}(\frac{1}{y^{3}+4y^{2}})
sum from n=0 to infinity of 2^{-n}	\sum\:_{n=0}^{\infty\:}2^{-n}
integral of (((ln(x))^3)/x)	\int\:(\frac{(\ln(x))^{3}}{x})dx
integral from 0 to 4 of sin(sqrt(x))	\int\:_{0}^{4}\sin(\sqrt{x})dx
(\partial)/(\partial y)(xy)	\frac{\partial\:}{\partial\:y}(xy)
integral of 2/3 (x+1)^{3/2}	\int\:\frac{2}{3}(x+1)^{\frac{3}{2}}dx
integral from 1 to 10 of 4	\int\:_{1}^{10}4dx
derivative of y=x-3	derivative\:y=x-3
(\partial)/(\partial y)(x^2y-2x^2-4y^2)	\frac{\partial\:}{\partial\:y}(x^{2}y-2x^{2}-4y^{2})
derivative of (4x-5)/(3x+2)	derivative\:\frac{4x-5}{3x+2}
derivative of (11x/((2+x^2)))	\frac{d}{dx}(\frac{11x}{(2+x^{2})})
area x=64-y^2,x=y^2-64	area\:x=64-y^{2},x=y^{2}-64
derivative of cos(5x-2)	\frac{d}{dx}(\cos(5x-2))
(\partial)/(\partial y)((2xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{2xy}{x^{2}+y^{2}})
integral of xsqrt(x^2+2x+4)	\int\:x\sqrt{x^{2}+2x+4}dx
(\partial)/(\partial x)(x^3sin(5y))	\frac{\partial\:}{\partial\:x}(x^{3}\sin(5y))
laplacetransform 2e^{-t}sin(2t)	laplacetransform\:2e^{-t}\sin(2t)
laplacetransform (1+te^{-t})^3	laplacetransform\:(1+te^{-t})^{3}
integral of (2sqrt(x))/(x-1)	\int\:\frac{2\sqrt{x}}{x-1}dx
t(dy)/(dt)+34y= 1/t	t\frac{dy}{dt}+34y=\frac{1}{t}
integral of (5-6x)*sin(4x)	\int\:(5-6x)\cdot\:\sin(4x)dx
integral from 1 to 4 of-10sqrt(x)ln(x)	\int\:_{1}^{4}-10\sqrt{x}\ln(x)dx
integral from 0 to 4 of arctan(x/4)	\int\:_{0}^{4}\arctan(\frac{x}{4})dx
(3y^2-x^2)/(y^5)(dy)/(dx)+x/(2y^4)=0	\frac{3y^{2}-x^{2}}{y^{5}}\frac{dy}{dx}+\frac{x}{2y^{4}}=0
integral of 7x^3cos(x^2)	\int\:7x^{3}\cos(x^{2})dx
xy^'+y=41sqrt(x)	xy^{\prime\:}+y=41\sqrt{x}
area 2-X^2,-X=Y	area\:2-X^{2},-X=Y
derivative of f(x)=(c^8-x^8)/(c^8+x^8)	derivative\:f(x)=\frac{c^{8}-x^{8}}{c^{8}+x^{8}}
derivative of e^{2x+3}	derivative\:e^{2x+3}
integral of 30-10t	\int\:30-10tdt
integral of zsqrt(z-1)	\int\:z\sqrt{z-1}dz
integral of e^{0.3x}	\int\:e^{0.3x}dx
y^{''}-2y^'+50y=0,y(0)= 3/2 ,y^'(0)=-9	y^{\prime\:\prime\:}-2y^{\prime\:}+50y=0,y(0)=\frac{3}{2},y^{\prime\:}(0)=-9
integral from 0 to 1-x of 24y(1-x-y)	\int\:_{0}^{1-x}24y(1-x-y)dy
derivative of 4y^2	derivative\:4y^{2}
tangent of y=(6x)/(x+3),(-1,-3)	tangent\:y=\frac{6x}{x+3},(-1,-3)
derivative of f(x)=(2sqrt(x))/(x^2-8)	derivative\:f(x)=\frac{2\sqrt{x}}{x^{2}-8}
integral of 1/(sqrt(t^2-2t+5))	\int\:\frac{1}{\sqrt{t^{2}-2t+5}}dt
limit as x approaches-1+of x+12	\lim\:_{x\to\:-1+}(x+12)
limit as x approaches 2 of x/(x-1)	\lim\:_{x\to\:2}(\frac{x}{x-1})
derivative of (2x)/((1-4x)^5)	derivative\:\frac{2x}{(1-4x)^{5}}
limit as x approaches 0+of (x+4)/x	\lim\:_{x\to\:0+}(\frac{x+4}{x})
integral of (e^{ln(1-t)})/(1-t)	\int\:\frac{e^{\ln(1-t)}}{1-t}dt
derivative of cot(2x)	\frac{d}{dx}(\cot(2x))
integral of e^{-x^2}x^3	\int\:e^{-x^{2}}x^{3}dx
derivative of 0.6e^{5x}	\frac{d}{dx}(0.6e^{5x})
derivative of xe^xln(x)	\frac{d}{dx}(xe^{x}\ln(x))
derivative of f(x)=sqrt(1-y^2)	derivative\:f(x)=\sqrt{1-y^{2}}
(dy)/(dx)-tan(x)y=e^{11x}	\frac{dy}{dx}-\tan(x)y=e^{11x}
sum from n=1 to infinity of 3/(n^6)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{6}}
derivative of ((x-3)/(sqrt(x)-\sqrt{3)})	\frac{d}{dx}(\frac{(x-3)}{\sqrt{x}-\sqrt{3}})
limit as x approaches 0 of (x^2-1)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}-1}{x^{2}})
derivative of (3x-8)/(sqrt(x))	derivative\:\frac{3x-8}{\sqrt{x}}
derivative of (e^x+e^{-x}/2)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{2})
y^{''}-10y^'+25y=0,y(0)=-3,y^'(0)=-29/2	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=0,y(0)=-3,y^{\prime\:}(0)=-\frac{29}{2}

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