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Popular Calculus Problems

area y=x^2-4,y=3x	area\:y=x^{2}-4,y=3x
derivative of (4x^2-1/2 x/(9x+8))	\frac{d}{dx}(\frac{4x^{2}-\frac{1}{2}x}{9x+8})
derivative of (1+1/x ^2)	\frac{d}{dx}((1+\frac{1}{x})^{2})
integral of (-x)^{2n}	\int\:(-x)^{2n}dx
derivative of f(x)=2t^{-3/4}	derivative\:f(x)=2t^{-\frac{3}{4}}
integral of te^{t^2}	\int\:te^{t^{2}}dt
derivative of (3x^2-5x-2/(4x+12))	\frac{d}{dx}(\frac{3x^{2}-5x-2}{4x+12})
(\partial)/(\partial y)(x^3-3x+y-e^y)	\frac{\partial\:}{\partial\:y}(x^{3}-3x+y-e^{y})
limit as x approaches 9 of (x^2-2)/(x-9)	\lim\:_{x\to\:9}(\frac{x^{2}-2}{x-9})
derivative of 5te^{-t/7}	derivative\:5te^{-\frac{t}{7}}
(\partial)/(\partial x)(e^{-x^8-y^4})	\frac{\partial\:}{\partial\:x}(e^{-x^{8}-y^{4}})
integral of 6sin^3(6x)cos^3(6x)	\int\:6\sin^{3}(6x)\cos^{3}(6x)dx
limit as x approaches infinity+of 3e^x	\lim\:_{x\to\:\infty\:+}(3e^{x})
integral of 7cos^3(4x)	\int\:7\cos^{3}(4x)dx
t^2y^'+y=sin(t),y(1)=0	t^{2}y^{\prime\:}+y=\sin(t),y(1)=0
(\partial)/(\partial y)((1-xy)^{-2})	\frac{\partial\:}{\partial\:y}((1-xy)^{-2})
integral of (x^6)/(sqrt(x^{14)-5)}	\int\:\frac{x^{6}}{\sqrt{x^{14}-5}}dx
derivative of f(x)=(3x+5)/(1-x^2)	derivative\:f(x)=\frac{3x+5}{1-x^{2}}
tangent of f(x)=(10x)/(x^2-6)	tangent\:f(x)=\frac{10x}{x^{2}-6}
integral of (x^5)/(e^{2-3x^6)}	\int\:\frac{x^{5}}{e^{2-3x^{6}}}dx
sum from n=1 to infinity of 1/(1-2n)	\sum\:_{n=1}^{\infty\:}\frac{1}{1-2n}
derivative of sqrt(3)t	derivative\:\sqrt{3}t
integral of x^2(x-2)^{1/2}	\int\:x^{2}(x-2)^{\frac{1}{2}}dx
derivative of sqrt(5)cos(x)	\frac{d}{dx}(\sqrt{5}\cos(x))
derivative of (x+1^{x^2+x^3})	\frac{d}{dx}((x+1)^{x^{2}+x^{3}})
integral of e^{sqrt(8x)}	\int\:e^{\sqrt{8x}}dx
sum from n=1 to infinity of \sqrt[n]{11}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{11}
ty^'-y=3t^2y^2	ty^{\prime\:}-y=3t^{2}y^{2}
tangent of 2x^3+3x^2-12x+6	tangent\:2x^{3}+3x^{2}-12x+6
integral of 1/(xsqrt(225x^2-225))	\int\:\frac{1}{x\sqrt{225x^{2}-225}}dx
integral of x/((sqrt(7^2-x^2))^3)	\int\:\frac{x}{(\sqrt{7^{2}-x^{2}})^{3}}dx
(\partial)/(\partial x)(e^y-3)	\frac{\partial\:}{\partial\:x}(e^{y}-3)
derivative of (2x^2-5^{-15})	\frac{d}{dx}((2x^{2}-5)^{-15})
tangent of f(x)=(x-5)^2,\at x=1	tangent\:f(x)=(x-5)^{2},\at\:x=1
integral from 0 to ln(4) of 3(4-xe^x)	\int\:_{0}^{\ln(4)}3(4-xe^{x})dx
(1+x^2)y^'=xy+x^2y^2	(1+x^{2})y^{\prime\:}=xy+x^{2}y^{2}
tangent of f(x)= 1/(sqrt(7x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{7x}},\at\:x=9
y^{''}-2xy^'=0	y^{\prime\:\prime\:}-2xy^{\prime\:}=0
integral from-2 to 6sqrt(2 of)2pi(y)(2)	\int\:_{-2}^{6\sqrt{2}}2π(y)(2)dy
integral of 2/(x^2-4x)	\int\:\frac{2}{x^{2}-4x}dx
laplacetransform sin(2t)*e^{3t}	laplacetransform\:\sin(2t)\cdot\:e^{3t}
derivative of arcsin(5x^4)	\frac{d}{dx}(\arcsin(5x^{4}))
integral of ln(2+x)	\int\:\ln(2+x)dx
slope ofintercept (-1,1),(1,-2)	slopeintercept\:(-1,1),(1,-2)
limit as x approaches 0 of (tan(2)(x))/x	\lim\:_{x\to\:0}(\frac{\tan(2)(x)}{x})
derivative of 2x^8e^x	derivative\:2x^{8}e^{x}
integral of 1/(4x)	\int\:\frac{1}{4x}dx
derivative of 4x^3+5x	\frac{d}{dx}(4x^{3}+5x)
derivative of arctan(5/x)	\frac{d}{dx}(\arctan(\frac{5}{x}))
derivative of (x^2+2x-2)/((x+1)^2)	derivative\:\frac{x^{2}+2x-2}{(x+1)^{2}}
(\partial)/(\partial z)(xze^{yz})	\frac{\partial\:}{\partial\:z}(xze^{yz})
y^'=0.23y-0.0005y^2	y^{\prime\:}=0.23y-0.0005y^{2}
integral from 0 to 60 of (60-y)^2	\int\:_{0}^{60}(60-y)^{2}dy
xy^'+y=3xsqrt(y)	xy^{\prime\:}+y=3x\sqrt{y}
integral from 1 to 10 of 1/(x^2)	\int\:_{1}^{10}\frac{1}{x^{2}}dx
derivative of x^2(sin(x))	derivative\:x^{2}(\sin(x))
(dy)/(dx)=y*(1/x-y)	\frac{dy}{dx}=y\cdot\:(\frac{1}{x}-y)
(\partial)/(\partial u)(sqrt(v/u))	\frac{\partial\:}{\partial\:u}(\sqrt{\frac{v}{u}})
derivative of ln(sqrt((9-x/(5+x))))	\frac{d}{dx}(\ln(\sqrt{\frac{9-x}{5+x}}))
derivative of-9x^2	derivative\:-9x^{2}
derivative of arccos(cos(x))	\frac{d}{dx}(\arccos(\cos(x)))
implicit (dy)/(dx),sqrt(xy)=x-2y	implicit\:\frac{dy}{dx},\sqrt{xy}=x-2y
(dy)/(dx)=((x-3))/(y-4)	\frac{dy}{dx}=\frac{(x-3)}{y-4}
integral of (289)/(x^3-17x^2)	\int\:\frac{289}{x^{3}-17x^{2}}dx
integral of (1-t)	\int\:(1-t)dt
limit as x approaches 0+of Inx	\lim\:_{x\to\:0+}(Inx)
integral of-1/(x-1)	\int\:-\frac{1}{x-1}dx
integral from 3 to x^3 of t^3	\int\:_{3}^{x^{3}}t^{3}dt
derivative of 1/(sqrt(x))	derivative\:\frac{1}{\sqrt{x}}
derivative of 1/3 sqrt(x)(x-3)	derivative\:\frac{1}{3}\sqrt{x}(x-3)
tangent of 2x^2-5x+3,\at x=0	tangent\:2x^{2}-5x+3,\at\:x=0
derivative of x^{tan(x)}	derivative\:x^{\tan(x)}
(dy)/(dx)=cos(y-x)	\frac{dy}{dx}=\cos(y-x)
integral from 0 to N of e^{-st}sin(5t)	\int\:_{0}^{N}e^{-st}\sin(5t)dt
inverse oflaplace 1/(s(2s+1))	inverselaplace\:\frac{1}{s(2s+1)}
derivative of sex+cos(x)	\frac{d}{dx}(sex+\cos(x))
integral of 2x(x^2+1)^6	\int\:2x(x^{2}+1)^{6}dx
derivative of cos(e^{-5x^5})	\frac{d}{dx}(\cos(e^{-5x^{5}}))
integral of (sqrt(8+tan(x)))/(1-sin^2(x))	\int\:\frac{\sqrt{8+\tan(x)}}{1-\sin^{2}(x)}dx
integral of 4/(t^2)	\int\:\frac{4}{t^{2}}dt
tangent of 22x^3	tangent\:22x^{3}
(\partial)/(\partial x)(sqrt(y+(cos^2(x))))	\frac{\partial\:}{\partial\:x}(\sqrt{y+(\cos^{2}(x))})
limit as x approaches 2 of sin(x)	\lim\:_{x\to\:2}(\sin(x))
derivative of sin^2(e^{3x+1})	\frac{d}{dx}(\sin^{2}(e^{3x+1}))
sum from n=0 to infinity of (3^n)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{3^{n}}
integral of (x^3)/(x^4-3)	\int\:\frac{x^{3}}{x^{4}-3}dx
integral from 0 to 2 of x^2-1	\int\:_{0}^{2}x^{2}-1dx
f(x)=-ln(x)	f(x)=-\ln(x)
integral of 5x^{-3}	\int\:5x^{-3}dx
d/(dy)(sin(y))	\frac{d}{dy}(\sin(y))
integral of e^{-x}sin(e^{-x})	\int\:e^{-x}\sin(e^{-x})dx
derivative of y=sqrt(x(x+11))	derivative\:y=\sqrt{x(x+11)}
integral of cos(nx)sin(nx)	\int\:\cos(nx)\sin(nx)dx
derivative of (15)/(ln(x))	derivative\:\frac{15}{\ln(x)}
integral of r^4	\int\:r^{4}dr
derivative of 2^{x^2-1}	\frac{d}{dx}(2^{x^{2}-1})
(\partial)/(\partial x)((F(c,x,b)cos(c))/(xb))	\frac{\partial\:}{\partial\:x}(\frac{F(c,x,b)\cdot\:\cos(c)}{x\cdot\:b})
derivative of sin(2cos(x))	\frac{d}{dx}(\sin(2\cos(x)))
derivative of (4x^5/((2x^3-2)^3))	\frac{d}{dx}(\frac{4x^{5}}{(2x^{3}-2)^{3}})
limit as x approaches 0-of 1/x*e^{1/x}	\lim\:_{x\to\:0-}(\frac{1}{x}\cdot\:e^{\frac{1}{x}})

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