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Popular Calculus Problems

limit as x approaches infinity of (4^x+3^x)^{1/x}	\lim\:_{x\to\:\infty\:}((4^{x}+3^{x})^{\frac{1}{x}})
integral from 1 to 5 of (5x-5/x)	\int\:_{1}^{5}(5x-\frac{5}{x})dx
limit as x approaches 3 of (x-4)/(x-3)	\lim\:_{x\to\:3}(\frac{x-4}{x-3})
integral of 5tan(x)sec^3(x)	\int\:5\tan(x)\sec^{3}(x)dx
limit as x approaches 4 of e^{4-x}	\lim\:_{x\to\:4}(e^{4-x})
(\partial)/(\partial x)(xy^3+x^2)	\frac{\partial\:}{\partial\:x}(xy^{3}+x^{2})
integral of ln(1+y)	\int\:\ln(1+y)dy
area x^4-x^2,1-x^2	area\:x^{4}-x^{2},1-x^{2}
derivative of cos^3(2+x)	\frac{d}{dx}(\cos^{3}(2+x))
derivative of (4-x^{1/(x-3)})	\frac{d}{dx}((4-x)^{\frac{1}{x-3}})
derivative of y=ln(sqrt(x+3))	derivative\:y=\ln(\sqrt{x+3})
y^{''}+9y=-sin(3t)	y^{\prime\:\prime\:}+9y=-\sin(3t)
area y=2x^3+3x^2-4x,y=x^2	area\:y=2x^{3}+3x^{2}-4x,y=x^{2}
y^{''}+4y^'+34y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+34y=0
derivative of f(x)= 2/(4x+3)	derivative\:f(x)=\frac{2}{4x+3}
integral from 1 to e^2 of (ln^6(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{6}(x^{2})}{x}dx
derivative of f(x)=(x-4)/(x+2)	derivative\:f(x)=\frac{x-4}{x+2}
tangent of x/(sqrt(36+x^2))	tangent\:\frac{x}{\sqrt{36+x^{2}}}
x^2ydy-xy^2dx-x^3y^2dx=0	x^{2}ydy-xy^{2}dx-x^{3}y^{2}dx=0
integral of (2x)/(1+2x^2)	\int\:\frac{2x}{1+2x^{2}}dx
tangent of f(x)=(5x-1)^4,\at x=2	tangent\:f(x)=(5x-1)^{4},\at\:x=2
(\partial)/(\partial x)(x^2*e^x)	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:e^{x})
area y=x^2,y= 2/((x^2+1))	area\:y=x^{2},y=\frac{2}{(x^{2}+1)}
integral of 1/(x^2)sqrt(2-1/x)	\int\:\frac{1}{x^{2}}\sqrt{2-\frac{1}{x}}dx
derivative of (19-(15-2x^4)^7)^3	derivative\:(19-(15-2x^{4})^{7})^{3}
(12x^2+y-1)dx-(6y-x)dy=0	(12x^{2}+y-1)dx-(6y-x)dy=0
xy^'+5y=0	xy^{\prime\:}+5y=0
extreme f(x)=e^{xy}	extreme\:f(x)=e^{xy}
limit as x approaches 0 of (5^x-1)/(7x)	\lim\:_{x\to\:0}(\frac{5^{x}-1}{7x})
integral from 0 to 1 of 1/(x^2+3x+2)	\int\:_{0}^{1}\frac{1}{x^{2}+3x+2}dx
integral of 49-x^2	\int\:49-x^{2}dx
xy^'-4y=x^5e^x	xy^{\prime\:}-4y=x^{5}e^{x}
integral of 1/(4+4x^2+x^4)	\int\:\frac{1}{4+4x^{2}+x^{4}}dx
simplify \sqrt[3]{3tan(x^2)}	simplify\:\sqrt[3]{3\tan(x^{2})}
integral of 56cos(8z-5)	\int\:56\cos(8z-5)dz
(\partial)/(\partial x)(sqrt(9-x^2-3y))	\frac{\partial\:}{\partial\:x}(\sqrt{9-x^{2}-3y})
sum from n=1 to infinity of (100)/n	\sum\:_{n=1}^{\infty\:}\frac{100}{n}
integral of e^{3x-2y}+x^2e^{-2y}	\int\:e^{3x-2y}+x^{2}e^{-2y}dx
integral of ((sin(x)+1)^{3/2})/(sec(x))	\int\:\frac{(\sin(x)+1)^{\frac{3}{2}}}{\sec(x)}dx
integral of sqrt(1+((3\sqrt{x))/2)^2}	\int\:\sqrt{1+(\frac{3\sqrt{x}}{2})^{2}}dx
tangent of f(x)=6x^2+2x-6	tangent\:f(x)=6x^{2}+2x-6
derivative of (x+1/(x-3))	\frac{d}{dx}(\frac{x+1}{x-3})
derivative of y=arcsin(6x+1)	derivative\:y=\arcsin(6x+1)
(d^3)/(dx^3)(3n^{-1/3}+2n^{5/3})	\frac{d^{3}}{dx^{3}}(3n^{-\frac{1}{3}}+2n^{\frac{5}{3}})
integral of 1/(sqrt(-2x^2-12x+32))	\int\:\frac{1}{\sqrt{-2x^{2}-12x+32}}dx
3t(dy)/(dt)+y=t^4	3t\frac{dy}{dt}+y=t^{4}
derivative of ln((e^x)/(1+e^x))	derivative\:\ln(\frac{e^{x}}{1+e^{x}})
simplify ln(sqrt((a^2-z^2)/(a^2+z^2)))	simplify\:\ln(\sqrt{\frac{a^{2}-z^{2}}{a^{2}+z^{2}}})
limit as x approaches 5 of (x-5)/(x-5)	\lim\:_{x\to\:5}(\frac{x-5}{x-5})
integral of 1/(4x^2-4x+5)	\int\:\frac{1}{4x^{2}-4x+5}dx
(dy)/(dx)tan(y)= 1/x	\frac{dy}{dx}\tan(y)=\frac{1}{x}
limit as x approaches 1 of 18x^{100}-5	\lim\:_{x\to\:1}(18x^{100}-5)
integral from 1 to 3 of (3x^2+4)	\int\:_{1}^{3}(3x^{2}+4)dx
integral of (x^3)/(sqrt(x^2-3))	\int\:\frac{x^{3}}{\sqrt{x^{2}-3}}dx
derivative of 80e^{-x/(10}-40x)	\frac{d}{dx}(80e^{-\frac{x}{10}}-40x)
(dy)/(dx)=(-0.1)/(cos(y)),y(0)= pi/2	\frac{dy}{dx}=\frac{-0.1}{\cos(y)},y(0)=\frac{π}{2}
inverse oflaplace ((2s+1))/(s^2)	inverselaplace\:\frac{(2s+1)}{s^{2}}
sum from n=0 to infinity of n*2^{n-1}	\sum\:_{n=0}^{\infty\:}n\cdot\:2^{n-1}
(\partial)/(\partial x)(x^4+y^4-4xy)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}-4xy)
(\partial)/(\partial x)(y^2e^{xyz})	\frac{\partial\:}{\partial\:x}(y^{2}e^{xyz})
limit as x approaches-infinity of-2	\lim\:_{x\to\:-\infty\:}(-2)
(\partial)/(\partial y)(3ycos(x))	\frac{\partial\:}{\partial\:y}(3y\cos(x))
(2xy+x^3)y^'= 1/2 x^2y+y^2	(2xy+x^{3})y^{\prime\:}=\frac{1}{2}x^{2}y+y^{2}
limit as x approaches-4 of 9x+11	\lim\:_{x\to\:-4}(9x+11)
integral of 30(1+sqrt(t))	\int\:30(1+\sqrt{t})dt
(\partial)/(\partial y)(x^3y+e^{xy^2})	\frac{\partial\:}{\partial\:y}(x^{3}y+e^{xy^{2}})
integral from 0 to 1 of ln(7x)	\int\:_{0}^{1}\ln(7x)dx
sum from n=0 to infinity of ((-1)^n7^nx^n)/(5^{n+1)}	\sum\:_{n=0}^{\infty\:}\frac{(-1)^{n}7^{n}x^{n}}{5^{n+1}}
integral from 2 to infinity of 2e^{-2x}	\int\:_{2}^{\infty\:}2e^{-2x}dx
integral of 2bx^3	\int\:2bx^{3}dx
derivative of (5x^2-7(3x^2-2x+1))	\frac{d}{dx}((5x^{2}-7)(3x^{2}-2x+1))
tangent of y= x/(sqrt(4-x)),(3,3)	tangent\:y=\frac{x}{\sqrt{4-x}},(3,3)
derivative of (x-2^2-ln(x))	\frac{d}{dx}((x-2)^{2}-\ln(x))
-1/(4x^{3/2)}	-\frac{1}{4x^{\frac{3}{2}}}
derivative of sin(1-x)	\frac{d}{dx}(\sin(1-x))
integral of (sin(2x))/(5+cos^2(x))	\int\:\frac{\sin(2x)}{5+\cos^{2}(x)}dx
limit as x approaches-infinity of-x^3	\lim\:_{x\to\:-\infty\:}(-x^{3})
(\partial)/(\partial y)(x^ay^{1-a})	\frac{\partial\:}{\partial\:y}(x^{a}y^{1-a})
d/(dy)(y+2+y(y+2)/2-((y+2)^2)/4)	\frac{d}{dy}(y+2+y\frac{y+2}{2}-\frac{(y+2)^{2}}{4})
limit as x approaches-4 of sqrt(x^2-16)	\lim\:_{x\to\:-4}(\sqrt{x^{2}-16})
derivative of 2e	\frac{d}{dx}(2e)
derivative of 6sin(x-2/(cos(x)))	\frac{d}{dx}(6\sin(x)-\frac{2}{\cos(x)})
limit as e^{e^x} approaches 0 of ((e^x)^{-2})/(e^x)	\lim\:_{e^{e^{x}}\to\:0}(\frac{(e^{x})^{-2}}{e^{x}})
integral from 0 to N of e^{-st}e^{4t}	\int\:_{0}^{N}e^{-st}e^{4t}dt
derivative of (-9/(2x^5))	\frac{d}{dx}(\frac{-9}{2x^{5}})
(dy)/(dx)=sqrt(1-y^2)	\frac{dy}{dx}=\sqrt{1-y^{2}}
tangent of f(x)=12sqrt(x),\at x=1	tangent\:f(x)=12\sqrt{x},\at\:x=1
(\partial)/(\partial y)((xyz^2)/(xy+1))	\frac{\partial\:}{\partial\:y}(\frac{xyz^{2}}{xy+1})
tangent of f(x)=sqrt(6x),(6,6)	tangent\:f(x)=\sqrt{6x},(6,6)
inverse oflaplace (30s+102)/(s^2+4s+40)	inverselaplace\:\frac{30s+102}{s^{2}+4s+40}
integral from 4 to infinity of e^{-4x}	\int\:_{4}^{\infty\:}e^{-4x}dx
derivative of (4x-2^2)	\frac{d}{dx}((4x-2)^{2})
(\partial}{\partial s}(\frac{(s-3r))/t)	\frac{\partial\:}{\partial\:s}(\frac{(s-3r)}{t})
derivative of sin^2(x+cos(x))	\frac{d}{dx}(\sin^{2}(x)+\cos(x))
integral of x^2sqrt(13x-1)	\int\:x^{2}\sqrt{13x-1}dx
integral of-1/(2y)	\int\:-\frac{1}{2y}dy
integral of-4sin^2(x)	\int\:-4\sin^{2}(x)dx
tangent of y= 1/(x^3),(-2,-1/8)	tangent\:y=\frac{1}{x^{3}},(-2,-\frac{1}{8})
limit as x approaches 3+of (1-2x)/(x-3)	\lim\:_{x\to\:3+}(\frac{1-2x}{x-3})
derivative of (14/(ln(x)))	\frac{d}{dx}(\frac{14}{\ln(x)})

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