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Popular Calculus Problems

sum from n=4 to infinity of 3-0.5^n	\sum\:_{n=4}^{\infty\:}3-0.5^{n}
y^'= x/(1+2y)	y^{\prime\:}=\frac{x}{1+2y}
integral of (20)/((x-4)(x^2+4))	\int\:\frac{20}{(x-4)(x^{2}+4)}dx
taylor sin(x),(3pi)/2	taylor\:\sin(x),\frac{3π}{2}
derivative of 100x-x^2	\frac{d}{dx}(100x-x^{2})
sum from n=1 to infinity of 3ne^{-n^2}	\sum\:_{n=1}^{\infty\:}3ne^{-n^{2}}
integral of (1+sqrt(9-x^2))	\int\:(1+\sqrt{9-x^{2}})dx
derivative of 4x^3-6x	\frac{d}{dx}(4x^{3}-6x)
laplacetransform 3-e^{2t}	laplacetransform\:3-e^{2t}
derivative of f(x)=2-sqrt(x)	derivative\:f(x)=2-\sqrt{x}
derivative of f(x)=(5x+1)/(x-1)	derivative\:f(x)=\frac{5x+1}{x-1}
area y=x^2-4,y=8-2x^2	area\:y=x^{2}-4,y=8-2x^{2}
(\partial)/(\partial y)(-3e^xcos(yz))	\frac{\partial\:}{\partial\:y}(-3e^{x}\cos(yz))
integral of (2x)/(x^2-7x+12)	\int\:\frac{2x}{x^{2}-7x+12}dx
(dy)/(dx)=(2+y)/(x+1)	\frac{dy}{dx}=\frac{2+y}{x+1}
tangent of f(x)=5x^2-x^3,(1,4)	tangent\:f(x)=5x^{2}-x^{3},(1,4)
f^'(x)=tan(x)	f^{\prime\:}(x)=\tan(x)
integral of (4x^2-19x-27)/((x+1)^2(x-3))	\int\:\frac{4x^{2}-19x-27}{(x+1)^{2}(x-3)}dx
derivative of log_{4}(x)	derivative\:\log_{4}(x)
derivative of f(x)=3x-2	derivative\:f(x)=3x-2
integral from 0 to pi of x^2sin(nx)	\int\:_{0}^{π}x^{2}\sin(nx)dx
integral of 6x^5e^{6x^6}	\int\:6x^{5}e^{6x^{6}}dx
integral of 6x+7	\int\:6x+7dx
integral of e^{3x}+2	\int\:e^{3x}+2dx
(\partial)/(\partial z)(x^2+y^2-z^2)	\frac{\partial\:}{\partial\:z}(x^{2}+y^{2}-z^{2})
integral from 1 to 7 of 5/(x^2)	\int\:_{1}^{7}\frac{5}{x^{2}}dx
integral of xln(2)+3/(2x)	\int\:x\ln(2)+\frac{3}{2x}dx
integral of 1/(sqrt(cos(x)-cos^2(x)))	\int\:\frac{1}{\sqrt{\cos(x)-\cos^{2}(x)}}dx
(\partial)/(\partial y)(-6xy-x^6-y^6)	\frac{\partial\:}{\partial\:y}(-6xy-x^{6}-y^{6})
derivative of ((4x+3)^8)/((x)^4)	derivative\:\frac{(4x+3)^{8}}{(x)^{4}}
limit as x approaches 0 of 6/(1+x)	\lim\:_{x\to\:0}(\frac{6}{1+x})
(\partial)/(\partial x)(e^{5x+3y})	\frac{\partial\:}{\partial\:x}(e^{5x+3y})
d/(dy)(1/t+1/(t^2)-y/(t^2+y^2))	\frac{d}{dy}(\frac{1}{t}+\frac{1}{t^{2}}-\frac{y}{t^{2}+y^{2}})
derivative of f(x)=1-1/(x^2)	derivative\:f(x)=1-\frac{1}{x^{2}}
integral of xcos(y)	\int\:x\cos(y)dy
tangent of x^2+y^2=169,(5,12)	tangent\:x^{2}+y^{2}=169,(5,12)
limit as x approaches 1 of 2-5/((x-1)^2)	\lim\:_{x\to\:1}(2-\frac{5}{(x-1)^{2}})
derivative of x(5x+3)^{1/3}	derivative\:x(5x+3)^{\frac{1}{3}}
integral of 8(x+1)In(x+1)	\int\:8(x+1)In(x+1)dx
sum from n=0 to infinity of z^{3n}	\sum\:_{n=0}^{\infty\:}z^{3n}
limit as x approaches infinity of (a_{n+1})/(a_{n)}	\lim\:_{x\to\:\infty\:}(\frac{a_{n+1}}{a_{n}})
(dr)/(dt)= 1/(t+1),r(0)=1	\frac{dr}{dt}=\frac{1}{t+1},r(0)=1
(1+x^2)y^'+1+2xy=0	(1+x^{2})y^{\prime\:}+1+2xy=0
integral of x^2(3-e^{x^3})	\int\:x^{2}(3-e^{x^{3}})dx
limit as x approaches infinity of e^{-2/(sqrt(x))}	\lim\:_{x\to\:\infty\:}(e^{-\frac{2}{\sqrt{x}}})
inverse oflaplace 2/s	inverselaplace\:\frac{2}{s}
integral from 1 to 2 of 0	\int\:_{1}^{2}0dx
integral from-infinity to-1 of x^{-11/5}	\int\:_{-\infty\:}^{-1}x^{-\frac{11}{5}}dx
integral of e^{3x}	\int\:e^{3x}dx
derivative of 3/(1+x^2)	\frac{d}{dx}(\frac{3}{1+x^{2}})
limit as x approaches 0 of (1-1x)^{1/x}	\lim\:_{x\to\:0}((1-1x)^{\frac{1}{x}})
derivative of x/(3sqrt(x^2+4))-1/4	derivative\:\frac{x}{3\sqrt{x^{2}+4}}-\frac{1}{4}
integral of (4x^2-8x)/((x-1)^2(x^2+1)^2)	\int\:\frac{4x^{2}-8x}{(x-1)^{2}(x^{2}+1)^{2}}dx
integral of sin(x)(1-cos(x))	\int\:\sin(x)(1-\cos(x))dx
derivative of (x^2-6x/(1+cos(x)))	\frac{d}{dx}(\frac{x^{2}-6x}{1+\cos(x)})
integral of 1/(x^2+4x+25)	\int\:\frac{1}{x^{2}+4x+25}dx
integral of xsqrt(4-x)	\int\:x\sqrt{4-x}dx
integral from 0 to 1 of 2y^2	\int\:_{0}^{1}2y^{2}dy
parity ln(e^{-x}+xe^{-x})	parity\:\ln(e^{-x}+xe^{-x})
derivative of (5x/(x-3))	\frac{d}{dx}(\frac{5x}{x-3})
y/(12000)+0.058y^'=0.0015	\frac{y}{12000}+0.058y^{\prime\:}=0.0015
limit as x approaches infinity of-18x^4	\lim\:_{x\to\:\infty\:}(-18x^{4})
derivative of y=-e^{-t}	derivative\:y=-e^{-t}
integral of ((x^2+2))/(x^4+4)	\int\:\frac{(x^{2}+2)}{x^{4}+4}dx
derivative of x(x^2+1^{-1/2})	\frac{d}{dx}(x(x^{2}+1)^{-\frac{1}{2}})
integral of (7x^2+5x-6)/((x^2-4)(x+2))	\int\:\frac{7x^{2}+5x-6}{(x^{2}-4)(x+2)}dx
f(x)=x^{4x}	f(x)=x^{4x}
limit as x approaches 1 of-6xsin(3x^2+1)	\lim\:_{x\to\:1}(-6x\sin(3x^{2}+1))
derivative of f(x)=(4x)/(x+2)	derivative\:f(x)=\frac{4x}{x+2}
derivative of (x^2+3^4(2x^3-5)^3)	\frac{d}{dx}((x^{2}+3)^{4}(2x^{3}-5)^{3})
(\partial)/(\partial x)(2x^2e^{xy^2})	\frac{\partial\:}{\partial\:x}(2x^{2}e^{xy^{2}})
derivative of y=log_{2}(5x)	derivative\:y=\log_{2}(5x)
taylor ln(x/2)2	taylor\:\ln(\frac{x}{2})2
integral from-1 to 1 of c(1-x^2)	\int\:_{-1}^{1}c(1-x^{2})dx
integral of (2x^2+3)/(x(x-1)^3)	\int\:\frac{2x^{2}+3}{x(x-1)^{3}}dx
(dy)/(dx)=(2y)/(x+1)	\frac{dy}{dx}=\frac{2y}{x+1}
limit as x approaches 1 of x+4	\lim\:_{x\to\:1}(x+4)
sum from n=1 to infinity of n/((5^n))	\sum\:_{n=1}^{\infty\:}\frac{n}{(5^{n})}
integral of x^2*sin(2x)	\int\:x^{2}\cdot\:\sin(2x)dx
derivative of (4x^2+1^{-50})	\frac{d}{dx}((4x^{2}+1)^{-50})
integral of ((x^2+3x-5)/(x-3))	\int\:(\frac{x^{2}+3x-5}{x-3})dx
integral of 2+x^2	\int\:2+x^{2}dx
derivative of y/(3x)	\frac{d}{dx}(\frac{y}{3x})
(dy)/(dx)=-2y,y(0)=3	\frac{dy}{dx}=-2y,y(0)=3
derivative of (3x^2+ln(x)*(5x^3)^x)	\frac{d}{dx}((3x^{2}+\ln(x))\cdot\:(5x^{3})^{x})
integral of 7sin^5(x)cos(x)	\int\:7\sin^{5}(x)\cos(x)dx
limit as x approaches infinity of (3x-2)/(6x+1)	\lim\:_{x\to\:\infty\:}(\frac{3x-2}{6x+1})
(d^2y)/(dt^2)	\frac{d^{2}y}{dt^{2}}
derivative of f(x)=arccot(e^x)	derivative\:f(x)=\arccot(e^{x})
derivative of y=x^2+x^{-2}+7x-1	derivative\:y=x^{2}+x^{-2}+7x-1
integral of x^3e^{3x^4}	\int\:x^{3}e^{3x^{4}}dx
derivative of tan(3x-4y)	\frac{d}{dx}(\tan(3x-4y))
(dy)/(dx)+2xy= x/(y^2)	\frac{dy}{dx}+2xy=\frac{x}{y^{2}}
derivative of (csc(x)^{-1})	\frac{d}{dx}((\csc(x))^{-1})
integral from 0 to 2 of 2pix(2x-x^2)	\int\:_{0}^{2}2πx(2x-x^{2})dx
integral of cot(18x)	\int\:\cot(18x)dx
derivative of x^2+10x	\frac{d}{dx}(x^{2}+10x)
inverse oflaplace 1/((s(s^2+1)))	inverselaplace\:\frac{1}{(s(s^{2}+1))}
d/(ds)(s^3)	\frac{d}{ds}(s^{3})
sum from n=0 to infinity of (5^n)/(6^n)	\sum\:_{n=0}^{\infty\:}\frac{5^{n}}{6^{n}}

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