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Popular Calculus Problems

derivative of 1/e e^x	\frac{d}{dx}(\frac{1}{e}e^{x})
derivative of 1/x+1/(x-1)+1/(x-2)	derivative\:\frac{1}{x}+\frac{1}{x-1}+\frac{1}{x-2}
integral of x^2*sin(x^3)	\int\:x^{2}\cdot\:\sin(x^{3})dx
sum from n=1 to infinity of 15(1/100)^n	\sum\:_{n=1}^{\infty\:}15(\frac{1}{100})^{n}
derivative of (x^2/2+1/x)	\frac{d}{dx}(\frac{x^{2}}{2}+\frac{1}{x})
derivative of sqrt(x)(x^5+2)	derivative\:\sqrt{x}(x^{5}+2)
limit as x approaches 0 of (2x^2+x)^x	\lim\:_{x\to\:0}((2x^{2}+x)^{x})
y^{''}+y= 1/((cos(2x))^{3/2)}	y^{\prime\:\prime\:}+y=\frac{1}{(\cos(2x))^{\frac{3}{2}}}
limit as x approaches 2+of (8+x)/(2-x)	\lim\:_{x\to\:2+}(\frac{8+x}{2-x})
integral of (10x^2)/(sqrt(1+x^3))	\int\:\frac{10x^{2}}{\sqrt{1+x^{3}}}dx
y^'=-y(3-ty)	y^{\prime\:}=-y(3-ty)
tangent of f(x)=sin(sin(x)),(4pi,0)	tangent\:f(x)=\sin(\sin(x)),(4π,0)
integral of 1/(sqrt(2x))	\int\:\frac{1}{\sqrt{2x}}dx
integral of x^2sec^2(x)	\int\:x^{2}\sec^{2}(x)dx
integral of (x+7)^2	\int\:(x+7)^{2}dx
integral of (x^2)/(sqrt(2+x^3))	\int\:\frac{x^{2}}{\sqrt{2+x^{3}}}dx
area x,(x^2)/4 ,0,2	area\:x,\frac{x^{2}}{4},0,2
2y^{'''}+3y^{''}-11y^'-6y=0	2y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}-11y^{\prime\:}-6y=0
integral of (24)/((144x^2+1)^2)	\int\:\frac{24}{(144x^{2}+1)^{2}}dx
integral from 0 to 9 of e^xsin(x)	\int\:_{0}^{9}e^{x}\sin(x)dx
integral from 0 to x of sqrt(3t+5)	\int\:_{0}^{x}\sqrt{3t+5}dt
laplacetransform e^{-t}+e^t	laplacetransform\:e^{-t}+e^{t}
y^{''}+4y^'+5y=5x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=5x+3e^{-x}
2t(dy)/(dt)+y=t^4	2t\frac{dy}{dt}+y=t^{4}
limit as x approaches-2-of 4x^2-7	\lim\:_{x\to\:-2-}(4x^{2}-7)
integral of (sin(2x))/(cos^2(x))	\int\:\frac{\sin(2x)}{\cos^{2}(x)}dx
limit as x approaches 0 of sin^2(x)	\lim\:_{x\to\:0}(\sin^{2}(x))
derivative of e^{3tsin(2t)}	derivative\:e^{3t\sin(2t)}
limit as x approaches 7+of ln(x^2-49)	\lim\:_{x\to\:7+}(\ln(x^{2}-49))
integral of 4x^9	\int\:4x^{9}dx
area y=sin^2(x),y=sin^3(x),x=0,x=pi	area\:y=\sin^{2}(x),y=\sin^{3}(x),x=0,x=π
y^{''}+400y=sec(20x)	y^{\prime\:\prime\:}+400y=\sec(20x)
limit as x approaches-3+of 4x^2-7	\lim\:_{x\to\:-3+}(4x^{2}-7)
integral of e^{2x}(x^2+2x)	\int\:e^{2x}(x^{2}+2x)dx
derivative of (t+4)^{(2/3)}(2t^2-4)^3	derivative\:(t+4)^{(\frac{2}{3})}(2t^{2}-4)^{3}
limit as x approaches 2 of sqrt(x^2+12)	\lim\:_{x\to\:2}(\sqrt{x^{2}+12})
(d^2)/(dx^2)(7/(8x^6))	\frac{d^{2}}{dx^{2}}(\frac{7}{8x^{6}})
tangent of f(x)=6x-32sqrt(x),\at x=4	tangent\:f(x)=6x-32\sqrt{x},\at\:x=4
derivative of f(x)=(x^2+sec(x))/(x-2e^x)	derivative\:f(x)=\frac{x^{2}+\sec(x)}{x-2e^{x}}
derivative of f(x)=(x^2+3)/x	derivative\:f(x)=\frac{x^{2}+3}{x}
(dy}{dx}(2y)+\frac{(1+y^2))/x =1	\frac{dy}{dx}(2y)+\frac{(1+y^{2})}{x}=1
(\partial)/(\partial t)(sin(x)cos(ct))	\frac{\partial\:}{\partial\:t}(\sin(x)\cos(ct))
integral of 18sin^2(x)cos^3(x)	\int\:18\sin^{2}(x)\cos^{3}(x)dx
derivative of arcsin(10x)	\frac{d}{dx}(\arcsin(10x))
integral from 2 to 3 of x+x^2	\int\:_{2}^{3}x+x^{2}dx
derivative of-(3x/(8-5x))	\frac{d}{dx}(-\frac{3x}{8-5x})
limit as n approaches infinity of (\sqrt[n]{n})/(ln(n))	\lim\:_{n\to\:\infty\:}(\frac{\sqrt[n]{n}}{\ln(n)})
limit as x approaches 4 of 4x+2x^2	\lim\:_{x\to\:4}(4x+2x^{2})
integral of cos^5(9-x)sin(9-x)	\int\:\cos^{5}(9-x)\sin(9-x)dx
integral of 1/(3x-x^2-2)	\int\:\frac{1}{3x-x^{2}-2}dx
integral of 3cot^5(θ)sin^4(θ)	\int\:3\cot^{5}(θ)\sin^{4}(θ)dθ
slope of x^2-2x+1	slope\:x^{2}-2x+1
derivative of \sqrt[3]{1-x^3+ln(x})	\frac{d}{dx}(\sqrt[3]{1-x^{3}+\ln(x)})
derivative of arctan(x-pi/2)	derivative\:\arctan(x-\frac{π}{2})
integral of x^3sqrt(x^2+35)	\int\:x^{3}\sqrt{x^{2}+35}dx
taylor e^{(x^3)}	taylor\:e^{(x^{3})}
area x^2,x=0,x=1	area\:x^{2},x=0,x=1
derivative of tan^2(sin^4(t))	derivative\:\tan^{2}(\sin^{4}(t))
inverse oflaplace 3/(s(s^2+8s+18))	inverselaplace\:\frac{3}{s(s^{2}+8s+18)}
limit as x approaches 2-of x^2-4	\lim\:_{x\to\:2-}(x^{2}-4)
integral from 1 to 5 of 2/(x^2+2x+1)	\int\:_{1}^{5}\frac{2}{x^{2}+2x+1}dx
integral of e^{-st}*(t^2-3t+1)	\int\:e^{-st}\cdot\:(t^{2}-3t+1)dt
derivative of ln(e^x+xe^x)	derivative\:\ln(e^{x}+xe^{x})
derivative of (3sqrt(x)+x(2-x^2))	\frac{d}{dx}((3\sqrt{x}+x)(2-x^{2}))
integral from 1 to 6 of 8x	\int\:_{1}^{6}8xdx
derivative of (5x)/(1+x^2)	derivative\:\frac{5x}{1+x^{2}}
(\partial)/(\partial x)(xy+x)	\frac{\partial\:}{\partial\:x}(xy+x)
derivative of-2sin(x+2sin(2x))	\frac{d}{dx}(-2\sin(x)+2\sin(2x))
integral of (cos(x)-sec(x))	\int\:(\cos(x)-\sec(x))dx
derivative of (t+5)^{2/3}(3t^2-2)^3	derivative\:(t+5)^{\frac{2}{3}}(3t^{2}-2)^{3}
(dy)/(dx)+5y=70,y(1)=110	\frac{dy}{dx}+5y=70,y(1)=110
limit as x approaches 10 of (7x^2-70x)/(x^2-100)	\lim\:_{x\to\:10}(\frac{7x^{2}-70x}{x^{2}-100})
integral of cos(0.5x)	\int\:\cos(0.5x)dx
taylor e^{-x/2}	taylor\:e^{-\frac{x}{2}}
derivative of te^t	derivative\:te^{t}
y^'-2y=x^2e^{2x}	y^{\prime\:}-2y=x^{2}e^{2x}
derivative of e^{5x-3}	\frac{d}{dx}(e^{5x-3})
integral of (1+x^2)^{1/2}	\int\:(1+x^{2})^{\frac{1}{2}}dx
integral of 2(sin(2x))^2	\int\:2(\sin(2x))^{2}dx
(\partial)/(\partial x)(xy*e^{xy})	\frac{\partial\:}{\partial\:x}(xy\cdot\:e^{xy})
derivative of 3x^2-e^x	\frac{d}{dx}(3x^{2}-e^{x})
integral of 4^tsin(4^t)	\int\:4^{t}\sin(4^{t})dt
derivative of sqrt(y-x+1)+sqrt(x-y+1)	\frac{d}{dx}(\sqrt{y-x+1}+\sqrt{x-y+1})
derivative of f(x)=ln(sqrt(x+9))	derivative\:f(x)=\ln(\sqrt{x+9})
derivative of-4ln(+1/x-4)	derivative\:-4\ln(+\frac{1}{x}-4)
(x^2+2y^2)dx=xydy	(x^{2}+2y^{2})dx=xydy
integral of (sin(1/(x^4)))/(x^5)	\int\:\frac{\sin(\frac{1}{x^{4}})}{x^{5}}dx
integral from 0.2 to 0.4 of 150x	\int\:_{0.2}^{0.4}150xdx
derivative of 5/(sqrt(x)+5)	derivative\:\frac{5}{\sqrt{x}+5}
y^'-(2x+1)y=0	y^{\prime\:}-(2x+1)y=0
integral of 1/(csc(x)(1+sin(x)))	\int\:\frac{1}{\csc(x)(1+\sin(x))}dx
integral from 0 to x of sqrt(1+36t)	\int\:_{0}^{x}\sqrt{1+36t}dt
integral from 1 to n of ln(x)	\int\:_{1}^{n}\ln(x)dx
derivative of (9+4x-6sqrt(x)/x)	\frac{d}{dx}(\frac{9+4x-6\sqrt{x}}{x})
(\partial)/(\partial x)(ln(x*cos(y)))	\frac{\partial\:}{\partial\:x}(\ln(x\cdot\:\cos(y)))
integral of 1/((x^2-441)^{3/2)}	\int\:\frac{1}{(x^{2}-441)^{\frac{3}{2}}}dx
y^{''}-2y^'+5y=e^{-2t}	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=e^{-2t}
integral of 3xe^{(-2x)}	\int\:3xe^{(-2x)}dx
(\partial)/(\partial y)(sqrt(5x+4y))	\frac{\partial\:}{\partial\:y}(\sqrt{5x+4y})
derivative of 7/(sqrt(x+1))	\frac{d}{dx}(\frac{7}{\sqrt{x+1}})

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