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Popular Calculus Problems

integral from 1 to 2 of x^3+1/(4x^3)	\int\:_{1}^{2}x^{3}+\frac{1}{4x^{3}}dx
limit as x approaches infinity of-7	\lim\:_{x\to\:\infty\:}(-7)
derivative of cos(x)-tan(x)	derivative\:\cos(x)-\tan(x)
(dy)/(dx)=-y^2	\frac{dy}{dx}=-y^{2}
limit as x approaches-2 of x^3-2x^2+4x+8	\lim\:_{x\to\:-2}(x^{3}-2x^{2}+4x+8)
limit as x approaches 0+of 5/(2x^4)	\lim\:_{x\to\:0+}(\frac{5}{2x^{4}})
derivative of (2x/((1-x^2)^2))	\frac{d}{dx}(\frac{2x}{(1-x^{2})^{2}})
integral from 2 to 5 of 3x^2-4x	\int\:_{2}^{5}3x^{2}-4xdx
(\partial)/(\partial y)(54-2/3 x^2-4y^2)	\frac{\partial\:}{\partial\:y}(54-\frac{2}{3}x^{2}-4y^{2})
sum from n=1 to infinity of n/(e^{n^3)}	\sum\:_{n=1}^{\infty\:}\frac{n}{e^{n^{3}}}
derivative of cos(-4t)	derivative\:\cos(-4t)
derivative of sin(x+1/2 cot(x))	\frac{d}{dx}(\sin(x)+\frac{1}{2}\cot(x))
derivative of y=sqrt(x+ln(3x))	derivative\:y=\sqrt{x+\ln(3x)}
integral from 0 to (3pi)/4 of sec^4(x/3)	\int\:_{0}^{\frac{3π}{4}}\sec^{4}(\frac{x}{3})dx
integral of 2rsqrt(1-r^2)	\int\:2r\sqrt{1-r^{2}}dr
derivative of (x^3+3x/(x^2+1))	\frac{d}{dx}(\frac{x^{3}+3x}{x^{2}+1})
xy^'+4y=x^3-x	xy^{\prime\:}+4y=x^{3}-x
integral of x\sqrt[4]{1-x^2}	\int\:x\sqrt[4]{1-x^{2}}dx
integral of t*e^{-t}	\int\:t\cdot\:e^{-t}dt
(y+ycos(xy))dx+(x+xcos(xy))dy=0	(y+y\cos(xy))dx+(x+x\cos(xy))dy=0
integral from 1 to e of ln(9x)	\int\:_{1}^{e}\ln(9x)dx
(\partial)/(\partial x)(x^5e^{xy}+3x)	\frac{\partial\:}{\partial\:x}(x^{5}e^{xy}+3x)
derivative of 3/(8x^{5/2)}	derivative\:\frac{3}{8x^{\frac{5}{2}}}
derivative of 4xy^3	\frac{d}{dx}(4xy^{3})
tangent of sqrt(x)(9.3)	tangent\:\sqrt{x}(9.3)
y^'=-y/t+2	y^{\prime\:}=-\frac{y}{t}+2
area f(x)=x^4-4x^2,g(x)=x^2-4	area\:f(x)=x^{4}-4x^{2},g(x)=x^{2}-4
integral of (6x+2)	\int\:(6x+2)dx
limit as x approaches-infinity of arccot(x)	\lim\:_{x\to\:-\infty\:}(\arccot(x))
derivative of e-x	\frac{d}{dx}(e-x)
derivative of-8/(x^3)	derivative\:-\frac{8}{x^{3}}
d/(dL)((2L+{K}(L))^{1/3})	\frac{d}{dL}((2L+{K}(L))^{\frac{1}{3}})
limit as x approaches 0 of x^2cos^2(2x)	\lim\:_{x\to\:0}(x^{2}\cos^{2}(2x))
integral from 0 to 2pi of-sin^2(x)	\int\:_{0}^{2π}-\sin^{2}(x)dx
limit as s approaches 0 of 4/(1+2^{1/s)}	\lim\:_{s\to\:0}(\frac{4}{1+2^{\frac{1}{s}}})
derivative of (sqrt(x)+1/(x^2+1))	\frac{d}{dx}(\frac{\sqrt{x}+1}{x^{2}+1})
derivative of 2xe^{-2x}-2x^2e^{-2x}	\frac{d}{dx}(2xe^{-2x}-2x^{2}e^{-2x})
((cos(x))/(sin(x)))^'	(\frac{\cos(x)}{\sin(x)})^{\prime\:}
derivative of \|x-3\|	\frac{d}{dx}(\left\|x-3\right\|)
tangent of y=sin(3x)+sin^2(3x),(0,0)	tangent\:y=\sin(3x)+\sin^{2}(3x),(0,0)
limit as x approaches infinity of 2,x	\lim\:_{x\to\:\infty\:}(2,x)
(\partial)/(\partial x)(6x^2+9xy+5y^2)	\frac{\partial\:}{\partial\:x}(6x^{2}+9xy+5y^{2})
((1+sin(x))^2+(1+cos(x))^4)^'	((1+\sin(x))^{2}+(1+\cos(x))^{4})^{\prime\:}
integral of (x+1)2	\int\:(x+1)2dx
y^'-4y=2xy^2	y^{\prime\:}-4y=2xy^{2}
derivative of ((x+3)/(x-3))	\frac{d}{dx}(\frac{(x+3)}{x-3})
derivative of x/(x+25)	derivative\:\frac{x}{x+25}
y^{''}+2y^'+5y=x	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=x
integral of 5/((x^2-1)^2)	\int\:\frac{5}{(x^{2}-1)^{2}}dx
derivative of 6/(x^4)	derivative\:\frac{6}{x^{4}}
integral of 2t^3-6t+7	\int\:2t^{3}-6t+7dt
derivative of (14x+6x^2/((7+6x)^2))	\frac{d}{dx}(\frac{14x+6x^{2}}{(7+6x)^{2}})
(\partial)/(\partial x)((-x-7y)/(y^2+6x^2))	\frac{\partial\:}{\partial\:x}(\frac{-x-7y}{y^{2}+6x^{2}})
derivative of (3x+2y^5)	\frac{d}{dx}((3x+2y)^{5})
integral from 0 to 4 of 5/(2x+1)	\int\:_{0}^{4}\frac{5}{2x+1}dx
derivative of 3^t	derivative\:3^{t}
maclaurin x*cos(2x)	maclaurin\:x\cdot\:\cos(2x)
simplify log_{5}(sqrt(x^2-1))	simplify\:\log_{5}(\sqrt{x^{2}-1})
tangent of y=(sqrt(2))^x	tangent\:y=(\sqrt{2})^{x}
(\partial)/(\partial x)(x^4cos(xy))	\frac{\partial\:}{\partial\:x}(x^{4}\cos(xy))
limit as x approaches infinity of 7	\lim\:_{x\to\:\infty\:}(7)
derivative of (e^x^{-1})	\frac{d}{dx}((e^{x})^{-1})
tangent of ((3x+5))/(1+x)	tangent\:\frac{(3x+5)}{1+x}
maclaurin ln(1+2x)	maclaurin\:\ln(1+2x)
integral of ln^3(2x)	\int\:\ln^{3}(2x)dx
derivative of 1/(sqrt(x-3))	derivative\:\frac{1}{\sqrt{x-3}}
derivative of ln(yx)	\frac{d}{dx}(\ln(yx))
xy^'-(1+x)y=xy^2	xy^{\prime\:}-(1+x)y=xy^{2}
limit as x approaches 1 of (x-1)/(sqrt(x+24)-5)	\lim\:_{x\to\:1}(\frac{x-1}{\sqrt{x+24}-5})
(\partial)/(\partial x)(2x+4)	\frac{\partial\:}{\partial\:x}(2x+4)
sum from n=1 to infinity of (n^4)/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{n^{4}}{n^{5}}
(\partial)/(\partial z)(2x-3yz)	\frac{\partial\:}{\partial\:z}(2x-3yz)
integral of (5x-4)/(sqrt(x^2+6x+13))	\int\:\frac{5x-4}{\sqrt{x^{2}+6x+13}}dx
derivative of \sqrt[4]{6x^4-7x^2}	\frac{d}{dx}(\sqrt[4]{6x^{4}-7x^{2}})
integral of 4x^3+3x^2+2x+1+1/x+1/(x^3)	\int\:4x^{3}+3x^{2}+2x+1+\frac{1}{x}+\frac{1}{x^{3}}dx
x^2y^{''}-2xy^'-4y=0	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}-4y=0
integral of (1/(x+1))	\int\:(\frac{1}{x+1})dx
derivative of (2a/x)	\frac{d}{dx}(\frac{2a}{x})
(\partial)/(\partial x)(7e^{-4x})	\frac{\partial\:}{\partial\:x}(7e^{-4x})
integral from 2 to 6 of f(x)	\int\:_{2}^{6}f(x)dx
slope of (2,3),(4,8)	slope\:(2,3),(4,8)
y^{''}+9y=0,y(0)=8,y^'(0)=7	y^{\prime\:\prime\:}+9y=0,y(0)=8,y^{\prime\:}(0)=7
inverse oflaplace (1/500)/(140+8s+s^2)	inverselaplace\:\frac{\frac{1}{500}}{140+8s+s^{2}}
integral of (sqrt(2x)-1/(sqrt(2x)))	\int\:(\sqrt{2x}-\frac{1}{\sqrt{2x}})dx
y^{''}+6.2832y=10	y^{\prime\:\prime\:}+6.2832y=10
derivative of y=x^2(x+3)	derivative\:y=x^{2}(x+3)
limit as x approaches infinity of 1.9	\lim\:_{x\to\:\infty\:}(1.9)
inverse oflaplace (0.001s)/(s^2+4)	inverselaplace\:\frac{0.001s}{s^{2}+4}
integral of (13x-6)/(x(3x-2))	\int\:\frac{13x-6}{x(3x-2)}dx
sum from n=1 to infinity of ((1^n))/n	\sum\:_{n=1}^{\infty\:}\frac{(1^{n})}{n}
derivative of (2xdx)	\frac{d}{dx}((2x)dx)
integral of (ln(y))/y	\int\:\frac{\ln(y)}{y}dy
derivative of x^2e^2	\frac{d}{dx}(x^{2}e^{2})
y^{''}-y^'-6y=e^{(-x)}	y^{\prime\:\prime\:}-y^{\prime\:}-6y=e^{(-x)}
integral of (x-1)/(x^2-2x+2)	\int\:\frac{x-1}{x^{2}-2x+2}dx
integral of 7/(7+e^x)	\int\:\frac{7}{7+e^{x}}dx
integral from 0 to 1 of sqrt(1+4y^2)	\int\:_{0}^{1}\sqrt{1+4y^{2}}dy
integral of 18xcos(1/2 x)	\int\:18x\cos(\frac{1}{2}x)dx
limit as x approaches 3-of f(x)x	\lim\:_{x\to\:3-}(f(x)x)
(\partial)/(\partial x)(ln(x+ct))	\frac{\partial\:}{\partial\:x}(\ln(x+ct))

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