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Popular Calculus Problems

derivative of e^{x-1}-1	\frac{d}{dx}(e^{x-1}-1)
(dy)/(dx)=x^8y	\frac{dy}{dx}=x^{8}y
integral of 1/(7+sqrt(2x))	\int\:\frac{1}{7+\sqrt{2x}}dx
integral of e^{2x}*cos(x)	\int\:e^{2x}\cdot\:\cos(x)dx
integral of 0.6x+2	\int\:0.6x+2dx
derivative of sqrt(19x)	derivative\:\sqrt{19x}
(\partial)/(\partial x)(xe^{sqrt(11xy)})	\frac{\partial\:}{\partial\:x}(xe^{\sqrt{11xy}})
longdivision ((x+1))/(x-1)	longdivision\:\frac{(x+1)}{x-1}
integral of 4e^3	\int\:4e^{3}dx
area y=-1+(x^2)/4 ,y=2+x/4 ,[0,4]	area\:y=-1+\frac{x^{2}}{4},y=2+\frac{x}{4},[0,4]
derivative of e^{-0.5x^2}	\frac{d}{dx}(e^{-0.5x^{2}})
integral of (2x^2+x)e^{3x}	\int\:(2x^{2}+x)e^{3x}dx
derivative of (5x+1^3(6x^2+3x+2)^5)	\frac{d}{dx}((5x+1)^{3}(6x^{2}+3x+2)^{5})
integral of cos((nxpi)/2)	\int\:\cos(\frac{nxπ}{2})dx
derivative of e^{-18x}	\frac{d}{dx}(e^{-18x})
(dy)/(dx)=0.5-x+2y	\frac{dy}{dx}=0.5-x+2y
integral from 1 to 8 of x/(sqrt(8+x^2))	\int\:_{1}^{8}\frac{x}{\sqrt{8+x^{2}}}dx
limit as x approaches-1-of \|x\|-3	\lim\:_{x\to\:-1-}(\left\|x\right\|-3)
integral of (e^{8x})/(e^{5x)}	\int\:\frac{e^{8x}}{e^{5x}}dx
slope of (0,-6),(5,-3)	slope\:(0,-6),(5,-3)
derivative of xcos(xy)	\frac{d}{dx}(x\cos(xy))
integral from 6 to 8 of 1/((x-6)^3)	\int\:_{6}^{8}\frac{1}{(x-6)^{3}}dx
taylor 1/(1-2x)	taylor\:\frac{1}{1-2x}
integral of (cos(2t))/((1+sin(2t))^4)	\int\:\frac{\cos(2t)}{(1+\sin(2t))^{4}}dt
y^3-(6x+6)+3xy^2y^'=0	y^{3}-(6x+6)+3xy^{2}y^{\prime\:}=0
limit as x approaches 0+of tan^{2x}(x)	\lim\:_{x\to\:0+}(\tan^{2x}(x))
laplacetransform e^{5t}sin(2t)	laplacetransform\:e^{5t}\sin(2t)
limit as x approaches+0 of (5^x-7^x)/x	\lim\:_{x\to\:+0}(\frac{5^{x}-7^{x}}{x})
y^'=-ay+by	y^{\prime\:}=-a\cdot\:y+b\cdot\:y
integral of (5^x)	\int\:(5^{x})dx
derivative of arcsinh(sqrt(x))	\frac{d}{dx}(\arcsinh(\sqrt{x}))
derivative of x^4-3x	derivative\:x^{4}-3x
limit as x approaches-0.1 of (e^x-1)/x	\lim\:_{x\to\:-0.1}(\frac{e^{x}-1}{x})
(dx)/(dt)=7xt^4	\frac{dx}{dt}=7xt^{4}
derivative of-(18/(ax))	\frac{d}{dx}(-\frac{18}{ax})
limit as x approaches 0+of sin(x)*ln(2x)	\lim\:_{x\to\:0+}(\sin(x)\cdot\:\ln(2x))
integral of (2x+5)^4	\int\:(2x+5)^{4}dx
derivative of y= 4/(3x^2)	derivative\:y=\frac{4}{3x^{2}}
f(x)=-(e^{1/x})/(x^2)	f(x)=-\frac{e^{\frac{1}{x}}}{x^{2}}
integral of (12x^2)/(sqrt(4x^3-1))	\int\:\frac{12x^{2}}{\sqrt{4x^{3}-1}}dx
integral of (4x+7)/((8x^2+28x)^3)	\int\:\frac{4x+7}{(8x^{2}+28x)^{3}}dx
integral of 5csc(x)	\int\:5\csc(x)dx
derivative of \sqrt[3]{x}+2sqrt(t^3)	\frac{d}{dx}(\sqrt[3]{x}+2\sqrt{t^{3}})
(\partial)/(\partial x)(lsin(θ))	\frac{\partial\:}{\partial\:x}(l\sin(θ))
derivative of ((cos^3(x)-1))/(cos^2(x))	derivative\:\frac{(\cos^{3}(x)-1)}{\cos^{2}(x)}
11(t+1)y^'-9y=18t	11(t+1)y^{\prime\:}-9y=18t
derivative of x/(x+b/x)	\frac{d}{dx}(\frac{x}{x+\frac{b}{x}})
(\partial)/(\partial x)(e^{x^{2-y^2}})	\frac{\partial\:}{\partial\:x}(e^{x^{2-y^{2}}})
derivative of y=ln(30)+30^{x+4}	derivative\:y=\ln(30)+30^{x+4}
integral of 3x-8	\int\:3x-8dx
(dQ)/(dt)=1-Q/(50)	\frac{dQ}{dt}=1-\frac{Q}{50}
derivative of (x^2/(sqrt(x-2y)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x-2y}})
integral of (3x)/(6x^2+9)	\int\:\frac{3x}{6x^{2}+9}dx
integral of (arcsin(x))/(sqrt(1-x))	\int\:\frac{\arcsin(x)}{\sqrt{1-x}}dx
derivative of (x^2/(x+7))	\frac{d}{dx}(\frac{x^{2}}{x+7})
sum from n=1 to infinity of sin(1/n)	\sum\:_{n=1}^{\infty\:}\sin(\frac{1}{n})
integral of sec^6(2x)	\int\:\sec^{6}(2x)dx
derivative of 1/(sqrt(u))	derivative\:\frac{1}{\sqrt{u}}
integral from 0 to 0.5 of tan(x)	\int\:_{0}^{0.5}\tan(x)dx
integral of (2x^3+x^2-6x+7)/(x^2+x-6)	\int\:\frac{2x^{3}+x^{2}-6x+7}{x^{2}+x-6}dx
slope of (-2.7)(20.16)	slope\:(-2.7)(20.16)
limit as x approaches 2-of x^2-1	\lim\:_{x\to\:2-}(x^{2}-1)
integral of \sqrt[3]{x}-4x	\int\:\sqrt[3]{x}-4xdx
limit as x approaches 0 of (1+ax)^{1/x}	\lim\:_{x\to\:0}((1+ax)^{\frac{1}{x}})
derivative of 3sin(x)ln(x)	derivative\:3\sin(x)\ln(x)
derivative of (x-sin(x)^5)	\frac{d}{dx}((x-\sin(x))^{5})
derivative of y= 1/3-6	derivative\:y=\frac{1}{3}-6
roots cosin(o)	roots\:co\sin(o)
derivative of (s^5-9)^2	derivative\:(s^{5}-9)^{2}
derivative of arctan(9x)	\frac{d}{dx}(\arctan(9x))
integral of 1/(xsqrt(x^2-1))	\int\:\frac{1}{x\sqrt{x^{2}-1}}dx
derivative of ((3x^7-7x^2+113)/((5x^3)))	\frac{d}{dx}(\frac{(3x^{7}-7x^{2}+113)}{(5x^{3})})
integral of 3x^2-5x+7/x+2e^3	\int\:3x^{2}-5x+\frac{7}{x}+2e^{3}dx
y^{''}-6y^'+9y=0,y(0)=2,y^'(0)=0	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=0
integral of 8/(4+x^2)	\int\:\frac{8}{4+x^{2}}dx
derivative of y=-2xsin(x^2)	derivative\:y=-2x\sin(x^{2})
inverse oflaplace (s-3)/(s^2-3s+2)	inverselaplace\:\frac{s-3}{s^{2}-3s+2}
limit as x approaches 10 of sqrt((10x)/(2x+5))	\lim\:_{x\to\:10}(\sqrt{\frac{10x}{2x+5}})
integral from 0 to infinity of 2xe^{-2x}	\int\:_{0}^{\infty\:}2xe^{-2x}dx
integral of (x^2+5)cos(3x)	\int\:(x^{2}+5)\cos(3x)dx
y^{''}=6x,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}=6x,y(0)=1,y^{\prime\:}(0)=-1
integral of 1/(sqrt(49-64x^2))	\int\:\frac{1}{\sqrt{49-64x^{2}}}dx
integral from-infinity to 0 of 1/(6-3x)	\int\:_{-\infty\:}^{0}\frac{1}{6-3x}dx
derivative of-6x	\frac{d}{dx}(-6x)
derivative of ln(x^6-1)	\frac{d}{dx}(\ln(x^{6}-1))
tangent of y=x^3,(2,8)	tangent\:y=x^{3},(2,8)
(\partial)/(\partial x)((x^3+x^4)(x^2+3x)^2)	\frac{\partial\:}{\partial\:x}((x^{3}+x^{4})(x^{2}+3x)^{2})
derivative of (3x-7^{12})	\frac{d}{dx}((3x-7)^{12})
integral of (x+1)/(2x)	\int\:\frac{x+1}{2x}dx
f(x)=e^x+ln(x)	f(x)=e^{x}+\ln(x)
derivative of y=5^{4x^2+3x}	derivative\:y=5^{4x^{2}+3x}
derivative of 9xy^2	derivative\:9xy^{2}
d/(dt)(ln(t+1))	\frac{d}{dt}(\ln(t+1))
xyy^'=1-x^2	xyy^{\prime\:}=1-x^{2}
integral of 1/((x^2-64)^{3/2)}	\int\:\frac{1}{(x^{2}-64)^{\frac{3}{2}}}dx
derivative of y= 1/(2sqrt(x))	derivative\:y=\frac{1}{2\sqrt{x}}
limit as x approaches 2 of (x+7)/(x^2-4)	\lim\:_{x\to\:2}(\frac{x+7}{x^{2}-4})
derivative of cos(arcsin(x+3))	derivative\:\cos(\arcsin(x+3))
integral of x(x-4)	\int\:x(x-4)dx
derivative of arctan(e^{2x})	\frac{d}{dx}(\arctan(e^{2x}))

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