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Popular Calculus Problems

taylor (1-x)e^{-x}	taylor\:(1-x)e^{-x}
inverse oflaplace 1/((s^2+9))	inverselaplace\:\frac{1}{(s^{2}+9)}
integral of (x^4-3x^2+5)/(x^4)	\int\:\frac{x^{4}-3x^{2}+5}{x^{4}}dx
limit as x approaches-2 of (x+2)/(2x)	\lim\:_{x\to\:-2}(\frac{x+2}{2x})
integral of xsin^2(x^2)	\int\:x\sin^{2}(x^{2})dx
integral of (e^x)/(e^{2x)+4e^x+3}	\int\:\frac{e^{x}}{e^{2x}+4e^{x}+3}dx
derivative of (sec(x)/(sqrt(x)))	\frac{d}{dx}(\frac{\sec(x)}{\sqrt{x}})
derivative of x^{cos(x)}	derivative\:x^{\cos(x)}
-5t^2y^{''}+ty^'+8y=0	-5t^{2}y^{\prime\:\prime\:}+ty^{\prime\:}+8y=0
area 3/x ,12x, 1/3 x	area\:\frac{3}{x},12x,\frac{1}{3}x
integral of rsqrt(1+4r^2)	\int\:r\sqrt{1+4r^{2}}dr
tangent of f(x)=cos(x),\at x= pi/4	tangent\:f(x)=\cos(x),\at\:x=\frac{π}{4}
derivative of x5^x	derivative\:x5^{x}
tangent of 2/(sqrt(x)),\at x=3	tangent\:\frac{2}{\sqrt{x}},\at\:x=3
integral of 2/(2x+1)	\int\:\frac{2}{2x+1}dx
sum from n=1 to infinity of 23(2/5)^n	\sum\:_{n=1}^{\infty\:}23(\frac{2}{5})^{n}
integral of (e^x)/(3-e^{2x)}	\int\:\frac{e^{x}}{3-e^{2x}}dx
y(x+3)+y^'=0	y(x+3)+y^{\prime\:}=0
tangent of 8+2x+xe^x	tangent\:8+2x+xe^{x}
tangent of f(x)=(4x)/(x+3),\at x=-5	tangent\:f(x)=\frac{4x}{x+3},\at\:x=-5
limit as x approaches 1.7 of sin(x)	\lim\:_{x\to\:1.7}(\sin(x))
integral of-(19)/(x^2+1)	\int\:-\frac{19}{x^{2}+1}dx
derivative of e^x+e^{-x}	derivative\:e^{x}+e^{-x}
limit as x approaches 2 of x^4+x^2-4	\lim\:_{x\to\:2}(x^{4}+x^{2}-4)
limit as x approaches 0 of (x^3+8)/(x+2)	\lim\:_{x\to\:0}(\frac{x^{3}+8}{x+2})
(\partial)/(\partial x)(2x^2y+cos(x^2))	\frac{\partial\:}{\partial\:x}(2x^{2}y+\cos(x^{2}))
derivative of (t^2-1)/(t^2+t-2)	derivative\:\frac{t^{2}-1}{t^{2}+t-2}
integral of 10x	\int\:10xdx
derivative of f(x)=-3e^{x^2+x-1}	derivative\:f(x)=-3e^{x^{2}+x-1}
x^2y^'+2xy=ln(x),y(1)=7	x^{2}y^{\prime\:}+2xy=\ln(x),y(1)=7
derivative of y=4+sqrt(x)	derivative\:y=4+\sqrt{x}
(d^2y)/(dx^2)+8(dy)/(dx)+16y=0	\frac{d^{2}y}{dx^{2}}+8\frac{dy}{dx}+16y=0
maclaurin cos(pix),0	maclaurin\:\cos(πx),0
derivative of (16)/x	derivative\:\frac{16}{x}
(\partial)/(\partial y)(3x^2)	\frac{\partial\:}{\partial\:y}(3x^{2})
derivative of x^5-5x	\frac{d}{dx}(x^{5}-5x)
integral of (x^2)/(x+4)	\int\:\frac{x^{2}}{x+4}dx
(1+ln(x)+y/x)dx+(1-ln(x))dy=0	(1+\ln(x)+\frac{y}{x})dx+(1-\ln(x))dy=0
d/(dt)(e^{2t}*y)	\frac{d}{dt}(e^{2t}\cdot\:y)
limit as x approaches 4 of ((2+x)^3-8)/x	\lim\:_{x\to\:4}(\frac{(2+x)^{3}-8}{x})
laplacetransform 2(s+2)	laplacetransform\:2(s+2)
integral of-3cos(x)+4sec^2(x)	\int\:-3\cos(x)+4\sec^{2}(x)dx
(\partial)/(\partial x)(4cos(4x))	\frac{\partial\:}{\partial\:x}(4\cos(4x))
taylor 1/(x+1)	taylor\:\frac{1}{x+1}
integral of (t+4)e^{t^2+8t+1}	\int\:(t+4)e^{t^{2}+8t+1}dt
y^{''}+8y^'=-256cos(8x)	y^{\prime\:\prime\:}+8y^{\prime\:}=-256\cos(8x)
y^'+2x^{-1}y=6x^4y^2	y^{\prime\:}+2x^{-1}y=6x^{4}y^{2}
integral of 3x^{-2/3}-2x^{5/3}	\int\:3x^{-\frac{2}{3}}-2x^{\frac{5}{3}}dx
integral of e^{(-1)/2 ln(x)}	\int\:e^{\frac{-1}{2}\ln(x)}dx
integral of 1/(u^2+9)	\int\:\frac{1}{u^{2}+9}du
derivative of log_{sqrt(e)}(sin(x))	\frac{d}{dx}(\log_{\sqrt{e}}(\sin(x)))
laplacetransform t(tcos(t)-sin(t))	laplacetransform\:t(t\cos(t)-\sin(t))
limit as x approaches 2 of (x^2-3x+2)/(x^2+5x-14)	\lim\:_{x\to\:2}(\frac{x^{2}-3x+2}{x^{2}+5x-14})
laplacetransform t^2*e^{-4t}	laplacetransform\:t^{2}\cdot\:e^{-4t}
integral of sin^4(x)cos^2(x)	\int\:\sin^{4}(x)\cos^{2}(x)dx
slope of (22,54),(62,27)	slope\:(22,54),(62,27)
(\partial)/(\partial x)(cos(x^2y^2))	\frac{\partial\:}{\partial\:x}(\cos(x^{2}y^{2}))
d/(dt)(sin(3t))	\frac{d}{dt}(\sin(3t))
integral of \sqrt[3]{x+1}	\int\:\sqrt[3]{x+1}dx
area y= 1/x ,y=0,x=1,x=e	area\:y=\frac{1}{x},y=0,x=1,x=e
integral of 5/((81+x^2)^{3/2)}	\int\:\frac{5}{(81+x^{2})^{\frac{3}{2}}}dx
derivative of 4/(x^6)	derivative\:\frac{4}{x^{6}}
(\partial)/(\partial x)(x/(x^7-y^5))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{7}-y^{5}})
limit as x approaches 0+of e^{3xln(x)}	\lim\:_{x\to\:0+}(e^{3x\ln(x)})
derivative of (arctan(6x))^2	derivative\:(\arctan(6x))^{2}
(dy)/(dx)=-x/y ,y(4)=3	\frac{dy}{dx}=-\frac{x}{y},y(4)=3
limit as x approaches pi/3 of (2cos^2(x)+3cos(x)-2)/(2cos(x)-1)	\lim\:_{x\to\:\frac{π}{3}}(\frac{2\cos^{2}(x)+3\cos(x)-2}{2\cos(x)-1})
derivative of f(x)=x^{-1/3}	derivative\:f(x)=x^{-\frac{1}{3}}
integral of e^{5x+4}	\int\:e^{5x+4}dx
integral of (1+x)/(sqrt(x))	\int\:\frac{1+x}{\sqrt{x}}dx
integral of (sqrt(x)+4)/(x^2)	\int\:\frac{\sqrt{x}+4}{x^{2}}dx
integral of sqrt(6+y)(y+2)^2	\int\:\sqrt{6+y}(y+2)^{2}dy
derivative of 6x^4sin(x)	\frac{d}{dx}(6x^{4}\sin(x))
(\partial)/(\partial x)(4x^2-8xy^4+7ay^5-3)	\frac{\partial\:}{\partial\:x}(4x^{2}-8xy^{4}+7ay^{5}-3)
taylor sin(x+1)	taylor\:\sin(x+1)
derivative of-1/2 cot(x)	\frac{d}{dx}(-\frac{1}{2}\cot(x))
(dy)/(dx)=e^xy^2	\frac{dy}{dx}=e^{x}y^{2}
derivative of y=(2x+5)/(3x-2)	derivative\:y=\frac{2x+5}{3x-2}
integral of (1+2x)	\int\:(1+2x)dx
derivative of f(x)=sec^6(x)	derivative\:f(x)=\sec^{6}(x)
inverse oflaplace ((2s-6))/(s^2+9)	inverselaplace\:\frac{(2s-6)}{s^{2}+9}
normal of y=2x^3-x^2+2,(1,3)	normal\:y=2x^{3}-x^{2}+2,(1,3)
derivative of cos(x^2)	derivative\:\cos(x^{2})
integral of 1/(sec(x^2))	\int\:\frac{1}{\sec(x^{2})}dx
integral of (e^{x/a}+1)^{1/3}e^{x/a}	\int\:(e^{\frac{x}{a}}+1)^{\frac{1}{3}}e^{\frac{x}{a}}dx
integral from 2 to 4 of (x(2x-3))/6	\int\:_{2}^{4}\frac{x(2x-3)}{6}dx
limit as x approaches 1-of 8/(sqrt(1-x))	\lim\:_{x\to\:1-}(\frac{8}{\sqrt{1-x}})
integral of (x^3+3x^2+6x+5)/(x^2+x+2)	\int\:\frac{x^{3}+3x^{2}+6x+5}{x^{2}+x+2}dx
f^'(x)=ln(x)	f^{\prime\:}(x)=\ln(x)
integral of 1/(xsqrt(x^2-36))	\int\:\frac{1}{x\sqrt{x^{2}-36}}dx
(\partial)/(\partial y)(y-y/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(y-\frac{y}{x^{2}+y^{2}})
(dN)/(dx)=((0.0922)N)(1-N/(60))	\frac{dN}{dx}=((0.0922)N)(1-\frac{N}{60})
derivative of (e^x-e^{-2x}^{1/5})	\frac{d}{dx}((e^{x}-e^{-2x})^{\frac{1}{5}})
derivative of ((3x-1)/(2x+1))	\frac{d}{dx}(\frac{(3x-1)}{2x+1})
integral of 4cos(sqrt(x))	\int\:4\cos(\sqrt{x})dx
derivative of f(x)=x^{3/2}+1/(x^{5/2)}	derivative\:f(x)=x^{\frac{3}{2}}+\frac{1}{x^{\frac{5}{2}}}
integral of ((e^t+2e^{2t}))/(e^{3t)}	\int\:\frac{(e^{t}+2e^{2t})}{e^{3t}}dt
(\partial)/(\partial x)(u/x)	\frac{\partial\:}{\partial\:x}(\frac{u}{x})
integral from-1 to 1 of 2sqrt(1-(x^2)/2)	\int\:_{-1}^{1}2\sqrt{1-\frac{x^{2}}{2}}dx
tangent of (12x)/(x^6)	tangent\:\frac{12x}{x^{6}}

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