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Popular Calculus Problems

limit as x approaches 3+of x^2	\lim\:_{x\to\:3+}(x^{2})
integral of 1/(x^3+3x^2)	\int\:\frac{1}{x^{3}+3x^{2}}dx
y^{''}-y^'-2y=-6t+10t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-6t+10t^{2}
inverse oflaplace (1+e^{-spi})/(s^2+1)	inverselaplace\:\frac{1+e^{-sπ}}{s^{2}+1}
derivative of y=3e^{3e^x+x}	derivative\:y=3e^{3e^{x}+x}
area tan(x),2sin(x),[-pi/3 , pi/3 ]	area\:\tan(x),2\sin(x),[-\frac{π}{3},\frac{π}{3}]
(\partial)/(\partial x)(e^{-2x})	\frac{\partial\:}{\partial\:x}(e^{-2x})
derivative of (4x^{3x})	\frac{d}{dx}((4x)^{3x})
area y=0,y=x^2,y=x+2	area\:y=0,y=x^{2},y=x+2
limit as x approaches infinity of \|2-x\|	\lim\:_{x\to\:\infty\:}(\left\|2-x\right\|)
derivative of 0.5(1-cos(x))	\frac{d}{dx}(0.5(1-\cos(x)))
(dy)/(dx)=sqrt(4y)e^{x+6}	\frac{dy}{dx}=\sqrt{4y}e^{x+6}
y^'-2xy=1	y^{\prime\:}-2xy=1
(\partial)/(\partial x)(2x^3+2xy^3)	\frac{\partial\:}{\partial\:x}(2x^{3}+2xy^{3})
integral of 1/(16x)	\int\:\frac{1}{16x}dx
(\partial)/(\partial x)(y^3sin(3x))	\frac{\partial\:}{\partial\:x}(y^{3}\sin(3x))
derivative of g(x)=((pi^2))/(x^2+4x)	derivative\:g(x)=\frac{(π^{2})}{x^{2}+4x}
derivative of sec(x-x)	\frac{d}{dx}(\sec(x)-x)
tangent of y=x^2+4x-11,(2,-1)	tangent\:y=x^{2}+4x-11,(2,-1)
taylor f(x)=sqrt(1+x),x=0	taylor\:f(x)=\sqrt{1+x},x=0
derivative of 2sqrt(1-x^2)	\frac{d}{dx}(2\sqrt{1-x^{2}})
limit as x approaches infinity of x^2+x	\lim\:_{x\to\:\infty\:}(x^{2}+x)
x^2(dy)/(dx)+xy=x^2e^x	x^{2}\frac{dy}{dx}+xy=x^{2}e^{x}
(11xy^2-13y)+(11x^2y-13x)*(dy)/(dx)=0	(11xy^{2}-13y)+(11x^{2}y-13x)\cdot\:\frac{dy}{dx}=0
derivative of f(x)=\sqrt[3]{x^4}	derivative\:f(x)=\sqrt[3]{x^{4}}
limit as x approaches+(-1) of-x^2+4x-5	\lim\:_{x\to\:+(-1)}(-x^{2}+4x-5)
(dy)/(dx)=4xsqrt(1-y^2)	\frac{dy}{dx}=4x\sqrt{1-y^{2}}
integral of (1-cos(x))	\int\:(1-\cos(x))dx
integral of 1/(e^{2x)+1}	\int\:\frac{1}{e^{2x}+1}dx
integral of sqrt((4-x)x)	\int\:\sqrt{(4-x)x}dx
y^'+3y=t+e^{(-2t)}	y^{\prime\:}+3y=t+e^{(-2t)}
limit as x approaches-3 of 1/((x+3)^2)	\lim\:_{x\to\:-3}(\frac{1}{(x+3)^{2}})
y^'-e^xe^y=-1	y^{\prime\:}-e^{x}e^{y}=-1
(\partial)/(\partial x)(e^{1+x^2-y^2})	\frac{\partial\:}{\partial\:x}(e^{1+x^{2}-y^{2}})
derivative of 6cos(2x-e^{-x})	\frac{d}{dx}(6\cos(2x)-e^{-x})
tangent of f(x)=2x^3+7x^2-8x-3,\at x=-1	tangent\:f(x)=2x^{3}+7x^{2}-8x-3,\at\:x=-1
limit as x approaches 1-of 1-x-[x]-[1-x]	\lim\:_{x\to\:1-}(1-x-[x]-[1-x])
limit as x approaches 4-of 1/((x-4)^2)	\lim\:_{x\to\:4-}(\frac{1}{(x-4)^{2}})
derivative of f(x)=x^{(7)}-3e^{(3x)}	derivative\:f(x)=x^{(7)}-3e^{(3x)}
limit as x approaches 0 of (1+4x)^{1/x}	\lim\:_{x\to\:0}((1+4x)^{\frac{1}{x}})
2y^{''}+3y^'-2y=25e^{-2x}	2y^{\prime\:\prime\:}+3y^{\prime\:}-2y=25e^{-2x}
slope ofintercept (-2,-1),(2,4)	slopeintercept\:(-2,-1),(2,4)
derivative of arctan(sqrt(6x^2-1))	derivative\:\arctan(\sqrt{6x^{2}-1})
integral of 8x*csc^2(4x)	\int\:8x\cdot\:\csc^{2}(4x)dx
integral of 2^{5x+2}	\int\:2^{5x+2}dx
2xy^'+y=6x,y(4)=15	2xy^{\prime\:}+y=6x,y(4)=15
derivative of \sqrt[3]{2x-7}	\frac{d}{dx}(\sqrt[3]{2x-7})
integral of (x')/(x^2)	\int\:\frac{x\prime\:}{x^{2}}dx
integral of tan^2(2x)	\int\:\tan^{2}(2x)dx
derivative of sin((2pix)/(33))	derivative\:\sin(\frac{2πx}{33})
(\partial)/(\partial x)(6xy+5yz+xz)	\frac{\partial\:}{\partial\:x}(6xy+5yz+xz)
(\partial)/(\partial x)(2xy-3xz^2)	\frac{\partial\:}{\partial\:x}(2xy-3xz^{2})
integral of 5sin^4(xco)s^2x	\int\:5\sin^{4}(xco)s^{2}xdx
derivative of (x^2+2x/(3x+6))	\frac{d}{dx}(\frac{x^{2}+2x}{3x+6})
limit as x approaches-1 of x^3-2	\lim\:_{x\to\:-1}(x^{3}-2)
parity cot^2(sin(θ))	parity\:\cot^{2}(\sin(θ))
derivative of x/u	derivative\:\frac{x}{u}
limit as x approaches 0 of (x^2+x)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}+x}{x^{2}})
laplacetransform-6t^2	laplacetransform\:-6t^{2}
integral of 3/(sqrt(1-t^2))	\int\:\frac{3}{\sqrt{1-t^{2}}}dt
(\partial)/(\partial x)(sqrt(xy)-xy)	\frac{\partial\:}{\partial\:x}(\sqrt{x\cdot\:y}-x\cdot\:y)
derivative of cos(x^2+1)	\frac{d}{dx}(\cos(x^{2}+1))
integral of x/(sqrt(x^2+6))	\int\:\frac{x}{\sqrt{x^{2}+6}}dx
integral of 10x^2	\int\:10x^{2}dx
integral of e^{7x}sin(5x)	\int\:e^{7x}\sin(5x)dx
(dy)/(dx)=-(y^2)/(1+y^2)*e^{-x}	\frac{dy}{dx}=-\frac{y^{2}}{1+y^{2}}\cdot\:e^{-x}
integral of x(2x+5)^{10}	\int\:x(2x+5)^{10}dx
integral of ln(x)x^3	\int\:\ln(x)x^{3}dx
integral of x(-cos(x+pi/3)+cos(x))	\int\:x(-\cos(x+\frac{π}{3})+\cos(x))dx
derivative of f(2x)^2-1	derivative\:f(2x)^{2}-1
factor x^5+2x^4-11x^3-12x^2+36x	factor\:x^{5}+2x^{4}-11x^{3}-12x^{2}+36x
derivative of-1/(x^2-7/x)	\frac{d}{dx}(-\frac{1}{x^{2}}-\frac{7}{x})
sum from n=9 to infinity of e^{5-4n}	\sum\:_{n=9}^{\infty\:}e^{5-4n}
area 4-x^2,-x+2	area\:4-x^{2},-x+2
derivative of e^2X	derivative\:e^{2}X
(dy)/(dx)=x(1+y^2)	\frac{dy}{dx}=x(1+y^{2})
(\partial)/(\partial x)(sin(x)cos(y))	\frac{\partial\:}{\partial\:x}(\sin(x)\cos(y))
(\partial)/(\partial y)(cos(x^2+xy))	\frac{\partial\:}{\partial\:y}(\cos(x^{2}+xy))
integral of a^u	\int\:a^{u}du
derivative of 3/(t^2)	derivative\:\frac{3}{t^{2}}
integral of cos^3(θ)	\int\:\cos^{3}(θ)dθ
(\partial)/(\partial x)(((x+y))/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{x-y})
integral from 0 to 1 of sqrt(1+x^4+2x^2)	\int\:_{0}^{1}\sqrt{1+x^{4}+2x^{2}}dx
integral of 1/((x+1)(x-2))	\int\:\frac{1}{(x+1)(x-2)}dx
integral from 6 to 8 of ((x^2+6)/(x^2))	\int\:_{6}^{8}(\frac{x^{2}+6}{x^{2}})dx
integral of (x^3-x^2+x-1)/(x^2+9)	\int\:\frac{x^{3}-x^{2}+x-1}{x^{2}+9}dx
derivative of (x+1)/(x^2)	derivative\:\frac{x+1}{x^{2}}
limit as x approaches 2 of log_{4}(x-2)	\lim\:_{x\to\:2}(\log_{4}(x-2))
(dy)/(dx)+3x^2y=x^2	\frac{dy}{dx}+3x^{2}y=x^{2}
(dy)/(dx)=10xe^{5y}	\frac{dy}{dx}=10xe^{5y}
derivative of f(x)= 2/(sqrt(x))	derivative\:f(x)=\frac{2}{\sqrt{x}}
derivative of sin^3(4x^2-1)	\frac{d}{dx}(\sin^{3}(4x^{2}-1))
limit as x approaches pi/2 of ln(sin(x))	\lim\:_{x\to\:\frac{π}{2}}(\ln(\sin(x)))
area 2/x ,8x, 1/2 x	area\:\frac{2}{x},8x,\frac{1}{2}x
limit as x approaches 3 of 2-x	\lim\:_{x\to\:3}(2-x)
derivative of 3t+5	derivative\:3t+5
derivative of (1-cos(x)/(1+sin(x)))	\frac{d}{dx}(\frac{1-\cos(x)}{1+\sin(x)})
derivative of-(e^{x-1}(x-3)/((x-1)^3))	\frac{d}{dx}(-\frac{e^{x-1}(x-3)}{(x-1)^{3}})
inverse oflaplace e^s 1/(s^2)	inverselaplace\:e^{s}\frac{1}{s^{2}}
derivative of e^{-8x^3}	\frac{d}{dx}(e^{-8x^{3}})

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