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Problemas populares de Cálculo

y^{''}+4y^'+18y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+18y=0,y(0)=1,y^{\prime\:}(0)=0
integral de (((ln(x))^3)/x)	\int\:(\frac{(\ln(x))^{3}}{x})dx
integral de 0 a 4 de sin(sqrt(x))	\int\:_{0}^{4}\sin(\sqrt{x})dx
(\partial)/(\partial y)(xy)	\frac{\partial\:}{\partial\:y}(xy)
integral de 3(x^3-x)	\int\:3(x^{3}-x)dx
integral de 2/3 (x+1)^{3/2}	\int\:\frac{2}{3}(x+1)^{\frac{3}{2}}dx
integral de 1 a 10 de 4	\int\:_{1}^{10}4dx
derivative y=x-3	derivative\:y=x-3
derivada de arctan((x-1/(x+1)))	\frac{d}{dx}(\arctan(\frac{x-1}{x+1}))
(\partial)/(\partial y)(x^2y-2x^2-4y^2)	\frac{\partial\:}{\partial\:y}(x^{2}y-2x^{2}-4y^{2})
derivative (4x-5)/(3x+2)	derivative\:\frac{4x-5}{3x+2}
derivada de (11x/((2+x^2)))	\frac{d}{dx}(\frac{11x}{(2+x^{2})})
área x=64-y^2,x=y^2-64	area\:x=64-y^{2},x=y^{2}-64
derivada de 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}})
límite cuando x tiende a+0 de (e^x+2x)^{1/(2x)}	\lim\:_{x\to\:+0}((e^{x}+2x)^{\frac{1}{2x}})
derivative f(x)=xln(x)-x	derivative\:f(x)=x\ln(x)-x
integral de 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))
laplacetransformación 2e^{-t}sin(2t)	laplacetransform\:2e^{-t}\sin(2t)
laplacetransformación (1+te^{-t})^3	laplacetransform\:(1+te^{-t})^{3}
integral de (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}
tangent f(x)=sqrt(x-1),\at x=5	tangent\:f(x)=\sqrt{x-1},\at\:x=5
integral de (5-6x)*sin(4x)	\int\:(5-6x)\cdot\:\sin(4x)dx
integral de 0 a 3 de 2x+1	\int\:_{0}^{3}2x+1dx
integral de 1 a 4 de-10sqrt(x)ln(x)	\int\:_{1}^{4}-10\sqrt{x}\ln(x)dx
integral de 0 a 4 de 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
límite cuando x tiende a 210 de 12x-350	\lim\:_{x\to\:210}(12x-350)
integral de 3 a e^5 de 1/x	\int\:_{3}^{e^{5}}\frac{1}{x}dx
(\partial)/(\partial x)(x^8+6xy^5)	\frac{\partial\:}{\partial\:x}(x^{8}+6xy^{5})
integral de 7x^3cos(x^2)	\int\:7x^{3}\cos(x^{2})dx
xy^'+y=41sqrt(x)	xy^{\prime\:}+y=41\sqrt{x}
derivative f(x)=sin^2(x)	derivative\:f(x)=\sin^{2}(x)
derivada de 2e^xcos(sqrt(2x))	\frac{d}{dx}(2e^{x}\cos(\sqrt{2x}))
área 2-X^2,-X=Y	area\:2-X^{2},-X=Y
derivada de xy+y	\frac{d}{dx}(xy+y)
derivative f(x)=(c^8-x^8)/(c^8+x^8)	derivative\:f(x)=\frac{c^{8}-x^{8}}{c^{8}+x^{8}}
derivative e^{2x+3}	derivative\:e^{2x+3}
integral de 30-10t	\int\:30-10tdt
integral de zsqrt(z-1)	\int\:z\sqrt{z-1}dz
integral de 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 de 0 a 1-x de 24y(1-x-y)	\int\:_{0}^{1-x}24y(1-x-y)dy
derivative 4y^2	derivative\:4y^{2}
integral de x*sin^3(x)	\int\:x\cdot\:\sin^{3}(x)dx
tangent y=(6x)/(x+3),(-1,-3)	tangent\:y=\frac{6x}{x+3},(-1,-3)
derivative f(x)=(2sqrt(x))/(x^2-8)	derivative\:f(x)=\frac{2\sqrt{x}}{x^{2}-8}
integral de 1/(sqrt(t^2-2t+5))	\int\:\frac{1}{\sqrt{t^{2}-2t+5}}dt
desarrollar (2x-7)(5-3x)	expand\:(2x-7)(5-3x)
límite cuando x tiende a-1+de x+12	\lim\:_{x\to\:-1+}(x+12)
(\partial)/(\partial x)(2e^xy)	\frac{\partial\:}{\partial\:x}(2e^{x}y)
y(dy)/(dx)=(y^2-y)(2x+5),y(1)=-3	y\frac{dy}{dx}=(y^{2}-y)(2x+5),y(1)=-3
integral de 0 a 6 de pi/4 (36-x^2)	\int\:_{0}^{6}\frac{π}{4}(36-x^{2})dx
límite cuando x tiende a 2 de x/(x-1)	\lim\:_{x\to\:2}(\frac{x}{x-1})
derivative (2x)/((1-4x)^5)	derivative\:\frac{2x}{(1-4x)^{5}}
integral de sin(θ)cos^2(θ)	\int\:\sin(θ)\cos^{2}(θ)dθ
límite cuando x tiende a 0+de (x+4)/x	\lim\:_{x\to\:0+}(\frac{x+4}{x})
d/(dy)(sqrt(xy))	\frac{d}{dy}(\sqrt{xy})
integral de (e^{ln(1-t)})/(1-t)	\int\:\frac{e^{\ln(1-t)}}{1-t}dt
límite cuando x tiende a 4+de (x-4)/(\|4-x\|)	\lim\:_{x\to\:4+}(\frac{x-4}{\left\|4-x\right\|})
derivada de cot(2x)	\frac{d}{dx}(\cot(2x))
pendiente (2.2)(-5.4)	slope\:(2.2)(-5.4)
integral de e^{-x^2}x^3	\int\:e^{-x^{2}}x^{3}dx
pendiente (0,14),(1,9)	slope\:(0,14),(1,9)
integral de e^{-5t}	\int\:e^{-5t}dt
derivada de ((e^x+e^{-x})/2)	\frac{d}{dx}(\frac{(e^{x}+e^{-x})}{2})
integral de (x^2-9)/(x-3)	\int\:\frac{x^{2}-9}{x-3}dx
derivada de (x^3+1^{1/3})	\frac{d}{dx}((x^{3}+1)^{\frac{1}{3}})
(\partial)/(\partial {K)}(-sqrt(2{K)^2+L^2})	\frac{\partial\:}{\partial\:{K}}(-\sqrt{2{K}^{2}+L^{2}})
integral de (2x-1)/(sqrt(x^2-7))	\int\:\frac{2x-1}{\sqrt{x^{2}-7}}dx
(\partial)/(\partial x)(zy)	\frac{\partial\:}{\partial\:x}(zy)
(\partial)/(\partial z)(x^3yz^2)	\frac{\partial\:}{\partial\:z}(x^{3}yz^{2})
derivada de 0.6e^{5x}	\frac{d}{dx}(0.6e^{5x})
derivada de xe^xln(x)	\frac{d}{dx}(xe^{x}\ln(x))
derivative f(x)=sqrt(1-y^2)	derivative\:f(x)=\sqrt{1-y^{2}}
límite cuando x tiende a 0+de 3/(e^x+1)	\lim\:_{x\to\:0+}(\frac{3}{e^{x}+1})
(dy)/(dx)-tan(x)y=e^{11x}	\frac{dy}{dx}-\tan(x)y=e^{11x}
y^{''}+4pi^2y=(cos(2pix))^3	y^{\prime\:\prime\:}+4π^{2}y=(\cos(2πx))^{3}
derivada de (k^2+x^2^k)	\frac{d}{dx}((k^{2}+x^{2})^{k})
serie de n=1 a infinity de 3/(n^6)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{6}}
derivada de ((x-3)/(sqrt(x)-\sqrt{3)})	\frac{d}{dx}(\frac{(x-3)}{\sqrt{x}-\sqrt{3}})
límite cuando x tiende a 0 de (x^2-1)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}-1}{x^{2}})
derivative (3x-8)/(sqrt(x))	derivative\:\frac{3x-8}{\sqrt{x}}
derivada de (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}
derivative f(x)=-(13)/(x^4)	derivative\:f(x)=-\frac{13}{x^{4}}
integral de 0 a 6 de k(6-x)	\int\:_{0}^{6}k(6-x)
inversalaplace (5(1-s^2))/((s+2)^3)	inverselaplace\:\frac{5(1-s^{2})}{(s+2)^{3}}
integral de ((2x+3))/((x+1)^2)	\int\:\frac{(2x+3)}{(x+1)^{2}}dx
(e^y+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0	(e^{y}+1)^{2}\cdot\:e^{-y}dx+(e^{x}+1)^{3}\cdot\:e^{-x}dy=0
integral de-1 a 1 de pi(6-6x^2)^2	\int\:_{-1}^{1}π(6-6x^{2})^{2}dx
integral de 0 a 2 de (4-x^2)	\int\:_{0}^{2}(4-x^{2})dx
derivative \sqrt[8]{x}+\sqrt[7]{x}	derivative\:\sqrt[8]{x}+\sqrt[7]{x}
(\partial)/(\partial x)(sqrt((x+4)/(y+5)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+4}{y+5}})
y^'= y/(xln(x))	y^{\prime\:}=\frac{y}{x\ln(x)}
tangent 110x-16x^2	tangent\:110x-16x^{2}
derivada de 16	\frac{d}{dx}(16)
integral de (7-6x^3+4x^6)/(x^6)	\int\:\frac{7-6x^{3}+4x^{6}}{x^{6}}dx

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