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Popular Calculus Problems

integral from 1 to 6 of x^{-4}	\int\:_{1}^{6}x^{-4}dx
integral of (3x^3)/(sqrt(49-x^2))	\int\:\frac{3x^{3}}{\sqrt{49-x^{2}}}dx
tangent of x^2-3x-2	tangent\:x^{2}-3x-2
derivative of arccos((x+1/3))	\frac{d}{dx}(\arccos(\frac{x+1}{3}))
y^'=x+y,y(0)=0	y^{\prime\:}=x+y,y(0)=0
integral of u^2	\int\:u^{2}du
integral from 0 to 3 of sqrt(3x)	\int\:_{0}^{3}\sqrt{3x}dx
derivative of 2-3x^2	\frac{d}{dx}(2-3x^{2})
(\partial)/(\partial y)(x^{3/4}y^{1/4})	\frac{\partial\:}{\partial\:y}(x^{\frac{3}{4}}y^{\frac{1}{4}})
area y=x^2,y=4	area\:y=x^{2},y=4
derivative of f(t)=e^{5tsin(2t)}	derivative\:f(t)=e^{5t\sin(2t)}
limit as x approaches 2 of 3x^4+4x^3-x+2	\lim\:_{x\to\:2}(3x^{4}+4x^{3}-x+2)
4y^{''}-4y^'+13y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}+13y=0
implicit (dy)/(dx),y=e^{4x^2+1}	implicit\:\frac{dy}{dx},y=e^{4x^{2}+1}
(\partial)/(\partial y)(yz)	\frac{\partial\:}{\partial\:y}(yz)
derivative of sqrt(x)-2sqrt(y)	\frac{d}{dx}(\sqrt{x}-2\sqrt{y})
integral of (sqrt(x))/(sqrt(x)+1)	\int\:\frac{\sqrt{x}}{\sqrt{x}+1}dx
derivative of log_{10}(3x)	derivative\:\log_{10}(3x)
integral of 1/((10+x)^2)	\int\:\frac{1}{(10+x)^{2}}dx
integral of x^3sqrt(3-x^2)	\int\:x^{3}\sqrt{3-x^{2}}dx
derivative of (x^6/(1-x^5))	\frac{d}{dx}(\frac{x^{6}}{1-x^{5}})
e^xy^'=2x	e^{x}y^{\prime\:}=2x
integral of 4/(sqrt(x^2+9))	\int\:\frac{4}{\sqrt{x^{2}+9}}dx
roots 6xy	roots\:6xy
integral of xsqrt(x-30)	\int\:x\sqrt{x-30}dx
integral from 0 to infinity of 8e^{-4x}	\int\:_{0}^{\infty\:}8e^{-4x}dx
integral from 0 to 5 of 1/4 (5-x)sqrt(x)	\int\:_{0}^{5}\frac{1}{4}(5-x)\sqrt{x}dx
d/(dt)({v}(t)t)	\frac{d}{dt}({v}(t)t)
(\partial)/(\partial x)(x^2-2xy)	\frac{\partial\:}{\partial\:x}(x^{2}-2xy)
(\partial)/(\partial x)(y^2x)	\frac{\partial\:}{\partial\:x}(y^{2}x)
integral of (4+x^2)/(sqrt(x))	\int\:\frac{4+x^{2}}{\sqrt{x}}dx
limit as x approaches-3 of x^2-9	\lim\:_{x\to\:-3}(x^{2}-9)
limit as x approaches 7-of 2/(x+7)	\lim\:_{x\to\:7-}(\frac{2}{x+7})
derivative of e^{(1/x})	\frac{d}{dx}(e^{(\frac{1}{x})})
derivative of ln\|tan(x\|)	\frac{d}{dx}(\ln\left\|\tan(x)\right\|)
area 1/(x+1),((x-1))/2 ,0,4	area\:\frac{1}{x+1},\frac{(x-1)}{2},0,4
derivative of 3x^x	\frac{d}{dx}(3x^{x})
xy+y^'=92x	xy+y^{\prime\:}=92x
derivative of sin(x/2-e^{-x^3})	\frac{d}{dx}(\sin(\frac{x}{2})-e^{-x^{3}})
(\partial)/(\partial x)((y/(x-y))^6)	\frac{\partial\:}{\partial\:x}((\frac{y}{x-y})^{6})
area x^2,\sqrt[3]{x}	area\:x^{2},\sqrt[3]{x}
derivative of x^{4^x}	derivative\:x^{4^{x}}
integral of 2y^2cos(9y)	\int\:2y^{2}\cos(9y)dy
slope of y^5+3x^2y^2+5x^4=49,(-1,2)	slope\:y^{5}+3x^{2}y^{2}+5x^{4}=49,(-1,2)
slope of (-5.3)(-1.5)	slope\:(-5.3)(-1.5)
limit as x approaches 5 of 5x+\|x-5\|	\lim\:_{x\to\:5}(5x+\left\|x-5\right\|)
y^{''}+2y^'+y=4e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e^{-t}
y^'=(ty^2-1)y,y(1)= 1/(sqrt(2))	y^{\prime\:}=(ty^{2}-1)y,y(1)=\frac{1}{\sqrt{2}}
integral of 1-e^{3x}	\int\:1-e^{3x}dx
tangent of f(x)= 3/x ,(3,1)	tangent\:f(x)=\frac{3}{x},(3,1)
x^2y^'+4xy=(sin(2x))/(x^2)	x^{2}y^{\prime\:}+4xy=\frac{\sin(2x)}{x^{2}}
derivative of Ce^{-x}	\frac{d}{dx}(Ce^{-x})
integral of w/((1+w)^{3/4)}	\int\:\frac{w}{(1+w)^{\frac{3}{4}}}dw
y^'=6x^2-3x^2y	y^{\prime\:}=6x^{2}-3x^{2}y
d/(dy)(x^{-2}y^{-5})	\frac{d}{dy}(x^{-2}y^{-5})
limit as x approaches 0 of 4/(sin(5x))	\lim\:_{x\to\:0}(\frac{4}{\sin(5x)})
y^'=-xe^{-x+y}	y^{\prime\:}=-xe^{-x+y}
integral of ((3x+5))/(x^2+2x+1)	\int\:\frac{(3x+5)}{x^{2}+2x+1}dx
(\partial)/(\partial x)(x+4)	\frac{\partial\:}{\partial\:x}(x+4)
integral of (-x)/(4+x^2)	\int\:\frac{-x}{4+x^{2}}dx
limit as x approaches 5 of-x^2+9x-7	\lim\:_{x\to\:5}(-x^{2}+9x-7)
derivative of (3x^5-1^7)	\frac{d}{dx}((3x^{5}-1)^{7})
integral of (e^u)/((3-e^u)^2)	\int\:\frac{e^{u}}{(3-e^{u})^{2}}du
integral from 1 to 2 of (1-t^2)t	\int\:_{1}^{2}(1-t^{2})tdt
tangent of f(x)=4x^3+8x,(-1,-12)	tangent\:f(x)=4x^{3}+8x,(-1,-12)
laplacetransform e^{(,\at)}	laplacetransform\:e^{(,\at\:)}
slope of (0,-4),(3,-7)	slope\:(0,-4),(3,-7)
inverse oflaplace (2s^3+3s^2-2s)/(s^3)	inverselaplace\:\frac{2s^{3}+3s^{2}-2s}{s^{3}}
derivative of m(t)=(4t+11)/(7t^2-3t+5)	derivative\:m(t)=\frac{4t+11}{7t^{2}-3t+5}
derivative of x/(x+y/x)	\frac{d}{dx}(\frac{x}{x+\frac{y}{x}})
integral of cos^8(x)sin(x)	\int\:\cos^{8}(x)\sin(x)dx
integral of cos(5t)	\int\:\cos(5t)dt
limit as x approaches 1-of 4x	\lim\:_{x\to\:1-}(4x)
y^'=0.05ln((2000)/y)y	y^{\prime\:}=0.05\ln(\frac{2000}{y})y
inverse oflaplace s/(s+8)	inverselaplace\:\frac{s}{s+8}
(\partial)/(\partial x)((x+y)*e^{x+2y})	\frac{\partial\:}{\partial\:x}((x+y)\cdot\:e^{x+2y})
area 4-(x-2)^2,5-(x-4)^2,2,4	area\:4-(x-2)^{2},5-(x-4)^{2},2,4
integral from 0 to 2 of (-x+2)^2	\int\:_{0}^{2}(-x+2)^{2}dx
integral of sqrt(4cos^2(2x)+4sin^2(2x))	\int\:\sqrt{4\cos^{2}(2x)+4\sin^{2}(2x)}dx
d/(dy)(e^{x^2-y^2})	\frac{d}{dy}(e^{x^{2}-y^{2}})
integral of-7x^3(6x^4+1)^6	\int\:-7x^{3}(6x^{4}+1)^{6}dx
limit as x approaches-infinity of 1/(4x)	\lim\:_{x\to\:-\infty\:}(\frac{1}{4x})
(\partial)/(\partial y)(e^z)	\frac{\partial\:}{\partial\:y}(e^{z})
sum from n=1 to infinity of (x^n)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{n+1}
d/(dy)(x^{(1+y)})	\frac{d}{dy}(x^{(1+y)})
derivative of (dy/(dx))+y=0	\frac{d}{dx}(\frac{dy}{dx})+y=0
limit as x approaches-1.8 of-3x+18.4	\lim\:_{x\to\:-1.8}(-3x+18.4)
y^'=e^{t+y}	y^{\prime\:}=e^{t+y}
(\partial)/(\partial x)(-3cos(x))	\frac{\partial\:}{\partial\:x}(-3\cos(x))
inverse oflaplace 1/(s(12s^2+10s+1))	inverselaplace\:\frac{1}{s(12s^{2}+10s+1)}
integral from 0 to 4 of (4x)^2-(x^2)^2	\int\:_{0}^{4}(4x)^{2}-(x^{2})^{2}dx
(\partial)/(\partial y)(ln(sqrt(3x)+5y))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{3x}+5y))
derivative of 5e^{-5x}	\frac{d}{dx}(5e^{-5x})
sum from n=0 to infinity of 2/(4n^2-1)	\sum\:_{n=0}^{\infty\:}\frac{2}{4n^{2}-1}
integral of (x+2)/(x^2+1)	\int\:\frac{x+2}{x^{2}+1}dx
derivative of y=sqrt(1-x^2)arcsin(x)	derivative\:y=\sqrt{1-x^{2}}\arcsin(x)
y^'=(x^2)	y^{\prime\:}=(x^{2})
y^'=((5xsec(y/x)+y))/x	y^{\prime\:}=\frac{(5x\sec(\frac{y}{x})+y)}{x}
derivative of y/(1-2x)	\frac{d}{dx}(\frac{y}{1-2x})
integral of (e^x+1)/2	\int\:\frac{e^{x}+1}{2}dx

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