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Popular Calculus Problems

integral of cos(x)ln(x)sin(x)	\int\:\cos(x)\ln(x)\sin(x)dx
integral of (2^x)/(2^x+3)	\int\:\frac{2^{x}}{2^{x}+3}dx
sum from n=0 to infinity of 5/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{5}{n+2}
derivative of y=x^4	derivative\:y=x^{4}
y^{''}+4y^'+5y=-5x+e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-5x+e^{-x}
derivative of y=(x^2)/((x+2))	derivative\:y=\frac{x^{2}}{(x+2)}
derivative of ln(x^8)	derivative\:\ln(x^{8})
integral of (sin^2(θ))/(cos^4(θ))	\int\:\frac{\sin^{2}(θ)}{\cos^{4}(θ)}dθ
(\partial)/(\partial x)(-(v(x,t))/(b(x,t)(x-v(x,t)t)))	\frac{\partial\:}{\partial\:x}(-\frac{v(x,t)}{b(x,t)(x-v(x,t)t)})
(dy)/y =dx	\frac{dy}{y}=dx
slope of 1/x	slope\:\frac{1}{x}
derivative of (1-xe^x)/(x+e^x)	derivative\:\frac{1-xe^{x}}{x+e^{x}}
(y^2-x^3-2x)dx+2xydy=0	(y^{2}-x^{3}-2x)dx+2xydy=0
limit as x approaches-2 of (10x)/(x^2)	\lim\:_{x\to\:-2}(\frac{10x}{x^{2}})
limit as x approaches 1 of x^2+3x+2	\lim\:_{x\to\:1}(x^{2}+3x+2)
integral of 1/(sqrt(1-cos(x)))	\int\:\frac{1}{\sqrt{1-\cos(x)}}dx
area x=-2,x=2,y=2x^2+12,y=0	area\:x=-2,x=2,y=2x^{2}+12,y=0
integral of (\sqrt[3]{x^5})	\int\:(\sqrt[3]{x^{5}})dx
integral of (x+1)/(x^2+1)	\int\:\frac{x+1}{x^{2}+1}dx
derivative of 8cosh(x/4 ln(arcsin(x)))	\frac{d}{dx}(8\cosh(\frac{x}{4})\ln(\arcsin(x)))
(d^2)/(dx^2)(2x^{-7})	\frac{d^{2}}{dx^{2}}(2x^{-7})
limit as x approaches 9 of 5x+\|x-9\|	\lim\:_{x\to\:9}(5x+\left\|x-9\right\|)
derivative of sqrt((4-x^2/4))	\frac{d}{dx}(\sqrt{\frac{4-x^{2}}{4}})
integral of 3^xx^2	\int\:3^{x}x^{2}dx
limit as x approaches 4 of x-3	\lim\:_{x\to\:4}(x-3)
derivative of 6/(x^6)	derivative\:\frac{6}{x^{6}}
limit as x approaches 6+of (\|x-6\|)/(x-6)	\lim\:_{x\to\:6+}(\frac{\left\|x-6\right\|}{x-6})
d/(dE)(Ei)	\frac{d}{dE}(Ei)
sum from n=1 to infinity of 2/(n^2+4n+3)	\sum\:_{n=1}^{\infty\:}\frac{2}{n^{2}+4n+3}
(\partial)/(\partial x)(x^4+2y^6-xy-x+2)	\frac{\partial\:}{\partial\:x}(x^{4}+2y^{6}-xy-x+2)
integral from 0 to 4 of pi(x+1)^2	\int\:_{0}^{4}π(x+1)^{2}dx
derivative of f(x)=x^3+2x-3	derivative\:f(x)=x^{3}+2x-3
tangent of x^2+y^2=50,(7,-1)	tangent\:x^{2}+y^{2}=50,(7,-1)
limit as x approaches+(-7) of-13	\lim\:_{x\to\:+(-7)}(-13)
limit as x approaches infinity of 3x^2	\lim\:_{x\to\:\infty\:}(3x^{2})
limit as x approaches 0+of x*e^{(1/x)}	\lim\:_{x\to\:0+}(x\cdot\:e^{(\frac{1}{x})})
derivative of ((3x-1/(5x+2))^4)	\frac{d}{dx}((\frac{3x-1}{5x+2})^{4})
integral from-1 to 4 of (x/(sqrt(5+x)))	\int\:_{-1}^{4}(\frac{x}{\sqrt{5+x}})dx
integral of (-7-7tan^2(x))	\int\:(-7-7\tan^{2}(x))dx
x(dy)/(dx)-3y=y^2,y(1)=3	x\frac{dy}{dx}-3y=y^{2},y(1)=3
integral of (-y)/(x^2+y^2)	\int\:\frac{-y}{x^{2}+y^{2}}dx
tangent of f(x)=3x^{2/3}-3,\at x=27	tangent\:f(x)=3x^{\frac{2}{3}}-3,\at\:x=27
derivative of 12x^{1/2}	\frac{d}{dx}(12x^{\frac{1}{2}})
integral of sin(9)	\int\:\sin(9)
integral of 1/(5-3x^2)	\int\:\frac{1}{5-3x^{2}}dx
integral of (e^y)/(e^y+1)	\int\:\frac{e^{y}}{e^{y}+1}dy
integral of 1/(5x^3-7x^2)	\int\:\frac{1}{5x^{3}-7x^{2}}dx
area x^2,x^k0,1	area\:x^{2},x^{k}0,1
integral from-infinity to 0 of 1/(7-3x)	\int\:_{-\infty\:}^{0}\frac{1}{7-3x}dx
integral of (20)/((100x^2+1)^2)	\int\:\frac{20}{(100x^{2}+1)^{2}}dx
d/(dt)(sin(t)-tcos(t))	\frac{d}{dt}(\sin(t)-t\cos(t))
9x^2y^2+x^{3/2}(dy)/(dx)=y^2	9x^{2}y^{2}+x^{\frac{3}{2}}\frac{dy}{dx}=y^{2}
derivative of x/(x^{-1)+7}	derivative\:\frac{x}{x^{-1}+7}
integral of (w^3)/(w+1)	\int\:\frac{w^{3}}{w+1}dw
derivative of 19arctan(sqrt(x))	\frac{d}{dx}(19\arctan(\sqrt{x}))
derivative of ln((6x^2+5)/(x^{4/5)})	derivative\:\ln(\frac{6x^{2}+5}{x^{\frac{4}{5}}})
inverse oflaplace (s+4)/(s^2+2s-3)	inverselaplace\:\frac{s+4}{s^{2}+2s-3}
derivative of 5x^2+2x+6	derivative\:5x^{2}+2x+6
(\partial}{\partial x}(\frac{x^2+y^2)/2)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+y^{2}}{2})
y^{''}-2/x y^'-(10)/(x^2)y=0	y^{\prime\:\prime\:}-\frac{2}{x}y^{\prime\:}-\frac{10}{x^{2}}y=0
derivative of cos(4x)	derivative\:\cos(4x)
tangent of sqrt(3x+4),\at x=4	tangent\:\sqrt{3x+4},\at\:x=4
derivative of (5x/((x^2+2)^2))	\frac{d}{dx}(\frac{5x}{(x^{2}+2)^{2}})
f(x)=e^xx+2e^x	f(x)=e^{x}x+2e^{x}
integral of 1/(xsqrt(x^2-12))	\int\:\frac{1}{x\sqrt{x^{2}-12}}dx
derivative of cos(xsec^2(x))	\frac{d}{dx}(\cos(x)\sec^{2}(x))
integral of (2-x^2)/((x^3-6x+1)^5)	\int\:\frac{2-x^{2}}{(x^{3}-6x+1)^{5}}dx
integral of (3x-1)^4	\int\:(3x-1)^{4}dx
integral from 0 to 1 of (37)/(x^p)	\int\:_{0}^{1}\frac{37}{x^{p}}dx
derivative of e^{3x^2}*6x	\frac{d}{dx}(e^{3x^{2}}\cdot\:6x)
tangent of y=2x^3+3x^2-12x+6	tangent\:y=2x^{3}+3x^{2}-12x+6
(d^2y)/(dt^2)+3(dy)/(dt)+y=1	\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}+y=1
limit as x approaches 2 of-10x+(10)	\lim\:_{x\to\:2}(-10x+(10))
derivative of f(x)=28x-0.01x^2	derivative\:f(x)=28x-0.01x^{2}
implicit 3x^2-5y^2=4	implicit\:3x^{2}-5y^{2}=4
derivative of 2x^3-12x^2-30x+9	derivative\:2x^{3}-12x^{2}-30x+9
derivative of 144	\frac{d}{dx}(144)
area 5-x^2,sin(x),-2,2	area\:5-x^{2},\sin(x),-2,2
integral of (sqrt((16-9x^2)))/x	\int\:\frac{\sqrt{(16-9x^{2})}}{x}dx
derivative of (-3x^6-x^5+3x^4)/(x^2)	derivative\:\frac{-3x^{6}-x^{5}+3x^{4}}{x^{2}}
sum from n=1 to infinity of (-1/2)^{n-1}	\sum\:_{n=1}^{\infty\:}(-\frac{1}{2})^{n-1}
derivative of-5/2 x^9	\frac{d}{dx}(-\frac{5}{2}x^{9})
integral from 0 to x of ln(x)	\int\:_{0}^{x}\ln(x)dx
(d^2)/(dx^2)(x^3+3x^2-2x+8)	\frac{d^{2}}{dx^{2}}(x^{3}+3x^{2}-2x+8)
(dy)/(dx)= x/y ,y(1)=2	\frac{dy}{dx}=\frac{x}{y},y(1)=2
derivative of (24)/(x^5)	derivative\:\frac{24}{x^{5}}
derivative of x/2-1	derivative\:\frac{x}{2}-1
(\partial)/(\partial x)(4-\|x\|-\|y\|)	\frac{\partial\:}{\partial\:x}(4-\left\|x\right\|-\left\|y\right\|)
integral of (x^3-3x+1)/(y+sqrt(y))	\int\:\frac{x^{3}-3x+1}{y+\sqrt{y}}dx
integral of (4e^{-0.8x})	\int\:(4e^{-0.8x})dx
(dx)/(dt)=e^{-kt}	\frac{dx}{dt}=e^{-kt}
area x^2,x^3	area\:x^{2},x^{3}
(\partial)/(\partial y)((x^2+y^2)^{3/2})	\frac{\partial\:}{\partial\:y}((x^{2}+y^{2})^{\frac{3}{2}})
(\partial)/(\partial x)(arctan(y/(x+a)))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{y}{x+a}))
tangent of f(x)=8x^2-x^3,\at x=1	tangent\:f(x)=8x^{2}-x^{3},\at\:x=1
integral of-x^2+5x-4	\int\:-x^{2}+5x-4dx
x*(dy)/(dx)+y= 1/(y^2)	x\cdot\:\frac{dy}{dx}+y=\frac{1}{y^{2}}
integral from 0 to e of x^2ln(x)	\int\:_{0}^{e}x^{2}\ln(x)dx
derivative of ln(x+e^x)	\frac{d}{dx}(\ln(x+e^{x}))
y^'=((1-y)^5)/4	y^{\prime\:}=\frac{(1-y)^{5}}{4}

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