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Popular Calculus Problems

integral of cot^5(6x)	\int\:\cot^{5}(6x)dx
(\partial)/(\partial x)(xe^{xy}+2xy+1/x)	\frac{\partial\:}{\partial\:x}(xe^{xy}+2xy+\frac{1}{x})
tangent of f(x)=2x^2-5x+3,\at x=0	tangent\:f(x)=2x^{2}-5x+3,\at\:x=0
integral of (8+sqrt(x)+x)/x	\int\:\frac{8+\sqrt{x}+x}{x}dx
(dx)/(dt)=xsin(t)	\frac{dx}{dt}=x\sin(t)
limit as x approaches 1-of arcsin(x)	\lim\:_{x\to\:1-}(\arcsin(x))
integral of x^2sqrt(x^3+4)	\int\:x^{2}\sqrt{x^{3}+4}dx
y^'-4y=6e^{6t}	y^{\prime\:}-4y=6e^{6t}
derivative of (c_{1}+c_{2}xe^{-3x})	\frac{d}{dx}((c_{1}+c_{2}x)e^{-3x})
limit as x approaches 0 of ((1+x^2)-1)/x	\lim\:_{x\to\:0}(\frac{(1+x^{2})-1}{x})
limit as x approaches pi/3 of sin(3x)	\lim\:_{x\to\:\frac{π}{3}}(\sin(3x))
sum from n=5 to infinity of e^{7-6n}	\sum\:_{n=5}^{\infty\:}e^{7-6n}
limit as x approaches infinity of x^2-3	\lim\:_{x\to\:\infty\:}(x^{2}-3)
derivative of e^x(1-y^2)	\frac{d}{dx}(e^{x}(1-y)^{2})
(ydy)/(dt)=(1+y^2)t^2	\frac{ydy}{dt}=(1+y^{2})t^{2}
(t+2)y^'+y=(1/(t-1))	(t+2)y^{\prime\:}+y=(\frac{1}{t-1})
limit as x approaches 5-of 5-x	\lim\:_{x\to\:5-}(5-x)
(\partial)/(\partial z)(4x^3+z^2)	\frac{\partial\:}{\partial\:z}(4x^{3}+z^{2})
derivative of 7x^4	derivative\:7x^{4}
x,sqrt(x),x=0,x=2	x,\sqrt{x},x=0,x=2
(\partial)/(\partial x)(cos^2(x))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x))
integral of (sin(x))^3(cos(x))^2	\int\:(\sin(x))^{3}(\cos(x))^{2}dx
derivative of ln(324sin^2(x))	\frac{d}{dx}(\ln(324\sin^{2}(x)))
(dy)/(dx)-5y=8	\frac{dy}{dx}-5y=8
(\partial)/(\partial x)(ye^{x/z})	\frac{\partial\:}{\partial\:x}(ye^{\frac{x}{z}})
integral of 4/(3x+2)	\int\:\frac{4}{3x+2}dx
limit as x approaches 2 of 4x-4.2	\lim\:_{x\to\:2}(4x-4.2)
(d^3)/(dx^3)(x^4-2x^3)	\frac{d^{3}}{dx^{3}}(x^{4}-2x^{3})
y^'=x^2+xy	y^{\prime\:}=x^{2}+xy
derivative of 4\sqrt[4]{x}	\frac{d}{dx}(4\sqrt[4]{x})
inverse oflaplace 1/((s+1)(s+1))	inverselaplace\:\frac{1}{(s+1)(s+1)}
(dy)/(dx)=(2x^3)/(2y+1)	\frac{dy}{dx}=\frac{2x^{3}}{2y+1}
2ty^'-y=0	2ty^{\prime\:}-y=0
integral of xsqrt(x^2+25)	\int\:x\sqrt{x^{2}+25}dx
integral of 5x^4y^3-x^2y^6+6x^5-4y	\int\:5x^{4}y^{3}-x^{2}y^{6}+6x^{5}-4ydx
derivative of (x^2+1/(x^2-1))	\frac{d}{dx}(\frac{x^{2}+1}{x^{2}-1})
limit as x approaches 0+of xln(x)	\lim\:_{x\to\:0+}(x\ln(x))
derivative of sin(6xcos(4x))	\frac{d}{dx}(\sin(6x)\cos(4x))
x^4+y^3sqrt(x^5+5)y^'=0	x^{4}+y^{3}\sqrt{x^{5}+5}y^{\prime\:}=0
3x^2y^2dx+2x^3ydy=0	3x^{2}y^{2}dx+2x^{3}ydy=0
integral of x\sqrt[3]{3-x^2}	\int\:x\sqrt[3]{3-x^{2}}dx
derivative of f(x)=sqrt(2-4x)	derivative\:f(x)=\sqrt{2-4x}
integral of 5/(\sqrt[3]{x^2)}+2/(sqrt(x^3))	\int\:\frac{5}{\sqrt[3]{x^{2}}}+\frac{2}{\sqrt{x^{3}}}dx
area 4,(e^x)/5 ,x=0	area\:4,\frac{e^{x}}{5},x=0
tangent of 5/(sqrt(x)),\at x= 1/4	tangent\:\frac{5}{\sqrt{x}},\at\:x=\frac{1}{4}
taylor cos(x-1)	taylor\:\cos(x-1)
d/(dt)(sin^2(e^{sin^2(t)}))	\frac{d}{dt}(\sin^{2}(e^{\sin^{2}(t)}))
(\partial}{\partial z}(\frac{z^2)/y)	\frac{\partial\:}{\partial\:z}(\frac{z^{2}}{y})
derivative of x^2-cos(2x)	\frac{d}{dx}(x^{2}-\cos(2x))
(12+x^2)y^'-2xy=0	(12+x^{2})y^{\prime\:}-2xy=0
limit as x approaches 0+of x^x	\lim\:_{x\to\:0+}(x^{x})
(\partial)/(\partial x)(x^6-8x^3y)	\frac{\partial\:}{\partial\:x}(x^{6}-8x^{3}y)
integral of λe^{-λt}	\int\:λe^{-λt}dt
sum from n=0 to infinity of (1/3)^{n-1}	\sum\:_{n=0}^{\infty\:}(\frac{1}{3})^{n-1}
(\partial)/(\partial x)(9e^xsqrt(x))	\frac{\partial\:}{\partial\:x}(9e^{x}\sqrt{x})
derivative of (2x-1(x+3))	\frac{d}{dx}((2x-1)(x+3))
integral of x/(sqrt(7x^2+6))	\int\:\frac{x}{\sqrt{7x^{2}+6}}dx
integral of 25e^{5θ}sin(5θ)	\int\:25e^{5θ}\sin(5θ)dθ
(2x-1)dx+(3y+4)dy=0	(2x-1)dx+(3y+4)dy=0
integral of (ln(x))/(xsqrt(1-ln(x)))	\int\:\frac{\ln(x)}{x\sqrt{1-\ln(x)}}dx
derivative of sqrt(15+x^2)	\frac{d}{dx}(\sqrt{15+x^{2}})
integral of 17arctan(sqrt(x))	\int\:17\arctan(\sqrt{x})dx
derivative of 8/(sqrt((9x^2-7^5)))	\frac{d}{dx}(\frac{8}{\sqrt{(9x^{2}-7)^{5}}})
integral of 5/(2+x^2)	\int\:\frac{5}{2+x^{2}}dx
(x^2+1)(dy)/(dx)+3xy=6x	(x^{2}+1)\frac{dy}{dx}+3xy=6x
limit as x approaches-infinity of e^xx^2	\lim\:_{x\to\:-\infty\:}(e^{x}x^{2})
integral of cos^9(x)sin(x)	\int\:\cos^{9}(x)\sin(x)dx
integral from 1 to 2 of 1/(xsqrt(x^2-1))	\int\:_{1}^{2}\frac{1}{x\sqrt{x^{2}-1}}dx
(\partial)/(\partial x)(((x-y))/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{(x-y)}{x^{2}+y^{2}})
(\partial)/(\partial y)(xye^{6y})	\frac{\partial\:}{\partial\:y}(xye^{6y})
integral of 1/(sin(u))	\int\:\frac{1}{\sin(u)}du
integral of (5+8x)/(1+x^2)	\int\:\frac{5+8x}{1+x^{2}}dx
integral of (3sec^2(4x)+3csc^2(4x))	\int\:(3\sec^{2}(4x)+3\csc^{2}(4x))dx
derivative of \sqrt[3]{x}-9/x	\frac{d}{dx}(\sqrt[3]{x}-\frac{9}{x})
sum from n=0 to infinity of 2+(0.1)^n	\sum\:_{n=0}^{\infty\:}2+(0.1)^{n}
integral of 1/2 tan(2x)	\int\:\frac{1}{2}\tan(2x)dx
derivative of sin(sqrt(cos(cot(3pix))))	\frac{d}{dx}(\sin(\sqrt{\cos(\cot(3πx))}))
derivative of 1/(5-4e^x)	\frac{d}{dx}(\frac{1}{5-4e^{x}})
integral of 2/(x^4-1)	\int\:\frac{2}{x^{4}-1}dx
limit as x approaches 4 of 9	\lim\:_{x\to\:4}(9)
limit as x approaches 0+of x/(1+x)	\lim\:_{x\to\:0+}(\frac{x}{1+x})
limit as x approaches 0 of vector	\lim\:_{x\to\:0}(vector)
limit as x approaches infinity of ln(4x)	\lim\:_{x\to\:\infty\:}(\ln(4x))
area 2x^2+4x-2,0,2	area\:2x^{2}+4x-2,0,2
derivative of sqrt(81-x^2)	derivative\:\sqrt{81-x^{2}}
(\partial)/(\partial y)(xe^{-x-y}sin(y))	\frac{\partial\:}{\partial\:y}(xe^{-x-y}\sin(y))
(\partial)/(\partial y)(xy^2e^y)	\frac{\partial\:}{\partial\:y}(xy^{2}e^{y})
f(x)=(5x^3+2)^4	f(x)=(5x^{3}+2)^{4}
derivative of tan(arcsin(x))	\frac{d}{dx}(\tan(\arcsin(x)))
(\partial)/(\partial x)(sin(x)+e^{xy})	\frac{\partial\:}{\partial\:x}(\sin(x)+e^{xy})
integral of ((5x-12))/(x^3-6x^2+8x)	\int\:\frac{(5x-12)}{x^{3}-6x^{2}+8x}dx
limit as x approaches 1-of 3/(x^3-1)	\lim\:_{x\to\:1-}(\frac{3}{x^{3}-1})
xy^'+y=6xy^2,y(1)=-8	xy^{\prime\:}+y=6xy^{2},y(1)=-8
integral from 2 to 13 of 1/(x^3-8)	\int\:_{2}^{13}\frac{1}{x^{3}-8}dx
integral of (3x+4)^{1/2}	\int\:(3x+4)^{\frac{1}{2}}dx
(xy^2+3y^2)dy-2xdx=0	(xy^{2}+3y^{2})dy-2xdx=0
derivative of 5/(sqrt(4+x))	\frac{d}{dx}(\frac{5}{\sqrt{4+x}})
slope of (4,1),(7,10)	slope\:(4,1),(7,10)
derivative of (18/x)	\frac{d}{dx}(\frac{18}{x})
(\partial)/(\partial y)(2cos(x)+cos(x+y))	\frac{\partial\:}{\partial\:y}(2\cos(x)+\cos(x+y))

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