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Popular Calculus Problems

integral from 0 to 3 of sqrt(10)	\int\:_{0}^{3}\sqrt{10}
integral of sqrt(x)-2^x-3sin(3x)+4e^{2x}	\int\:\sqrt{x}-2^{x}-3\sin(3x)+4e^{2x}dx
integral of (x^3)/(x^2+6x+5)	\int\:\frac{x^{3}}{x^{2}+6x+5}dx
(dy)/(dx)-2xy=2x	\frac{dy}{dx}-2xy=2x
xy^'=y+5x^2sin(x),y(pi)=0	xy^{\prime\:}=y+5x^{2}\sin(x),y(π)=0
(\partial)/(\partial x)(yx^2)	\frac{\partial\:}{\partial\:x}(yx^{2})
integral of 8/(sqrt(x+8)+\sqrt{x)}	\int\:\frac{8}{\sqrt{x+8}+\sqrt{x}}dx
derivative of f(z)=e^{z/((z-1))}	derivative\:f(z)=e^{\frac{z}{(z-1)}}
(dy)/(dx)= x/(2y^2)	\frac{dy}{dx}=\frac{x}{2y^{2}}
limit as x approaches 8+of (7-x)/(8-x)	\lim\:_{x\to\:8+}(\frac{7-x}{8-x})
(dy)/(dx)=(cos(11x))/(e^{11y)}	\frac{dy}{dx}=\frac{\cos(11x)}{e^{11y}}
limit as x approaches 5 of 3/((x-5)^2)	\lim\:_{x\to\:5}(\frac{3}{(x-5)^{2}})
derivative of 1-sqrt(x)	derivative\:1-\sqrt{x}
inverse oflaplace (s+7)/(s^2-3s-10)	inverselaplace\:\frac{s+7}{s^{2}-3s-10}
derivative of (e^{2x}/(x^8))	\frac{d}{dx}(\frac{e^{2x}}{x^{8}})
e^{xy}dx+y/x e^{xy}dy=0	e^{xy}dx+\frac{y}{x}e^{xy}dy=0
integral from 0 to 1 of 3(1+sqrt(x))^7	\int\:_{0}^{1}3(1+\sqrt{x})^{7}dx
derivative of sqrt(1-x^2)arcsin(x)	derivative\:\sqrt{1-x^{2}}\arcsin(x)
d/(dy)(arctan(sqrt((x-y)/x)))	\frac{d}{dy}(\arctan(\sqrt{\frac{x-y}{x}}))
(\partial)/(\partial x)(((x-y))/(c(a-b)))	\frac{\partial\:}{\partial\:x}(\frac{(x-y)}{c(a-b)})
d/(dt)(8t)	\frac{d}{dt}(8t)
integral of 5/3	\int\:\frac{5}{3}dx
integral from 6 to 8 of x/(x^2+6x+13)	\int\:_{6}^{8}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial x)(ln(8x))	\frac{\partial\:}{\partial\:x}(\ln(8x))
derivative of ((e^x-1)/((e^x+1)))	\frac{d}{dx}(\frac{(e^{x}-1)}{(e^{x}+1)})
(\partial)/(\partial x)(ln(5x+2y))	\frac{\partial\:}{\partial\:x}(\ln(5x+2y))
limit as x approaches 6 of 1	\lim\:_{x\to\:6}(1)
maclaurin ln(1+x),\at (x=2)	maclaurin\:\ln(1+x),\at\:(x=2)
tangent of 3x^2-4x	tangent\:3x^{2}-4x
taylor e^{x-1},0	taylor\:e^{x-1},0
y+sin(x)=x^3y^'	y+\sin(x)=x^{3}y^{\prime\:}
integral of e^{4y}	\int\:e^{4y}dy
limit as x approaches 0+of x^{6x}	\lim\:_{x\to\:0+}(x^{6x})
derivative of f(x)=sqrt(x)+\sqrt[3]{x}	derivative\:f(x)=\sqrt{x}+\sqrt[3]{x}
derivative of sqrt(s)	derivative\:\sqrt{s}
integral of sqrt(400-x^2)	\int\:\sqrt{400-x^{2}}dx
area 5cos(3x),5sin(6x),[0, pi/6 ]	area\:5\cos(3x),5\sin(6x),[0,\frac{π}{6}]
laplacetransform cos(t+pi)	laplacetransform\:\cos(t+π)
derivative of 2x^3+3x^2-12x+9	derivative\:2x^{3}+3x^{2}-12x+9
limit as x approaches 0+of (1-x)^{1/x}	\lim\:_{x\to\:0+}((1-x)^{\frac{1}{x}})
(dy)/(dx)=3x^2+1	\frac{dy}{dx}=3x^{2}+1
limit as x approaches 0-of 1/(sqrt(x))	\lim\:_{x\to\:0-}(\frac{1}{\sqrt{x}})
integral of ((sin(5x))/(cos(5x)))	\int\:(\frac{\sin(5x)}{\cos(5x)})dx
derivative of tan(3t)	derivative\:\tan(3t)
integral of (x^2-4x+3)/(x(x+1)^2)	\int\:\frac{x^{2}-4x+3}{x(x+1)^{2}}dx
integral of x^5e^{x^6+1}	\int\:x^{5}e^{x^{6}+1}dx
taylor \|x\|	taylor\:\left\|x\right\|
derivative of 1/6 (e^{3x}+e^{-3x})	\frac{d}{dx}(\frac{1}{6}(e^{3x}+e^{-3x}))
(dx)/(dt)=3x(5-x)	\frac{dx}{dt}=3x(5-x)
(\partial)/(\partial x)(x/(x^2-2x))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}-2x})
normal of f(x)= 1/(x^2),(-1,1)	normal\:f(x)=\frac{1}{x^{2}},(-1,1)
y^'=0.3y(1-y/(2500))-120	y^{\prime\:}=0.3y(1-\frac{y}{2500})-120
inverse oflaplace (6s+3)/(s^4+5s^2+4)	inverselaplace\:\frac{6s+3}{s^{4}+5s^{2}+4}
xy^'+4y=8x^4	xy^{\prime\:}+4y=8x^{4}
integral of e^{-t}t	\int\:e^{-t}tdt
integral of 27x^7+3x^5-45x^3+sqrt(2x)	\int\:27x^{7}+3x^{5}-45x^{3}+\sqrt{2x}dx
limit as x approaches 0 of sin(x)-x	\lim\:_{x\to\:0}(\sin(x)-x)
integral of (1/(xsqrt(x)))	\int\:(\frac{1}{x\sqrt{x}})dx
integral of x/(2x^2+8x+11)	\int\:\frac{x}{2x^{2}+8x+11}dx
(\partial)/(\partial z)(sqrt(x^y+ln(z)))	\frac{\partial\:}{\partial\:z}(\sqrt{x^{y}+\ln(z)})
integral of (2x-2)	\int\:(2x-2)dx
(\partial)/(\partial x)(3x^2y+y^2+yz)	\frac{\partial\:}{\partial\:x}(3x^{2}y+y^{2}+yz)
derivative of (6x/(x^2-3))	\frac{d}{dx}(\frac{6x}{x^{2}-3})
limit as x approaches-5 of (x^3+125)/(x^2-25)	\lim\:_{x\to\:-5}(\frac{x^{3}+125}{x^{2}-25})
integral of (x-2)/(x+7)	\int\:\frac{x-2}{x+7}dx
integral from 0 to 9 of \|x^2-6x+5\|	\int\:_{0}^{9}\left\|x^{2}-6x+5\right\|dx
limit as x approaches 1-of (\|x-1\|)/(1-x)	\lim\:_{x\to\:1-}(\frac{\left\|x-1\right\|}{1-x})
derivative of y=8e^{8e^x+x}	derivative\:y=8e^{8e^{x}+x}
integral of ((cos(x)))/x	\int\:\frac{(\cos(x))}{x}dx
(d^3)/(dx^3)(sin(x^3))	\frac{d^{3}}{dx^{3}}(\sin(x^{3}))
integral of cos(5x-7)	\int\:\cos(5x-7)dx
integral of 1/(sqrt(x^2+2x+26))	\int\:\frac{1}{\sqrt{x^{2}+2x+26}}dx
derivative of 4x^3-100x^2+600x	\frac{d}{dx}(4x^{3}-100x^{2}+600x)
(\partial)/(\partial x)(sin(5x))	\frac{\partial\:}{\partial\:x}(\sin(5x))
integral of (6x-1)cos(x)	\int\:(6x-1)\cos(x)dx
derivative of x^{ln(2})	\frac{d}{dx}(x^{\ln(2)})
tangent of f(x)=sqrt(5x+11),\at x=5	tangent\:f(x)=\sqrt{5x+11},\at\:x=5
derivative of-7x^2	\frac{d}{dx}(-7x^{2})
inverse oflaplace (5s+12)/(s+3)	inverselaplace\:\frac{5s+12}{s+3}
integral of (2x+2)^3	\int\:(2x+2)^{3}dx
inverse oflaplace 2/((s^2-2s+9))	inverselaplace\:\frac{2}{(s^{2}-2s+9)}
derivative of-5x^{1/3}	\frac{d}{dx}(-5x^{\frac{1}{3}})
d/(dt)(e^t(sin(t)+cos(t)))	\frac{d}{dt}(e^{t}(\sin(t)+\cos(t)))
y^{'''}+5y^{''}-8y^'-48y=0	y^{\prime\:\prime\:\prime\:}+5y^{\prime\:\prime\:}-8y^{\prime\:}-48y=0
integral of e-xcos(2x)	\int\:e-x\cos(2x)dx
integral of (e^{ax+b}-e^{bx+a})/(e^{ax)}	\int\:\frac{e^{ax+b}-e^{bx+a}}{e^{ax}}dx
-9y^{''}+81y=0	-9y^{\prime\:\prime\:}+81y=0
sum from n=0 to infinity of ((2^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(2^{n})}{n!}
inverse oflaplace (28)/((s^2+11))	inverselaplace\:\frac{28}{(s^{2}+11)}
limit as x approaches 1 of 3x^4+3x^2-x+2	\lim\:_{x\to\:1}(3x^{4}+3x^{2}-x+2)
(d^2y)/(dt^2)-5(dy)/(dt)+6y=0	\frac{d^{2}y}{dt^{2}}-5\frac{dy}{dt}+6y=0
(\partial)/(\partial x)(ln(x^5+y^5))	\frac{\partial\:}{\partial\:x}(\ln(x^{5}+y^{5}))
laplacetransform e^{-1(t+1)}	laplacetransform\:e^{-1(t+1)}
integral of e^{0.5x}	\int\:e^{0.5x}dx
integral of e^{-2x+3}	\int\:e^{-2x+3}dx
taylor x^2e^{2x}	taylor\:x^{2}e^{2x}
derivative of 7/4 x^2-3x+12	derivative\:\frac{7}{4}x^{2}-3x+12
derivative of 4+7sqrt(x)	derivative\:4+7\sqrt{x}
taylor sin(θ)	taylor\:\sin(θ)
integral of sin(2x)sin(3x)	\int\:\sin(2x)\sin(3x)dx

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