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Popular Calculus Problems

limit as x approaches 7 of (3x+2)^{2/3}	\lim\:_{x\to\:7}((3x+2)^{\frac{2}{3}})
integral from 0 to 1 of (1-x)^2x	\int\:_{0}^{1}(1-x)^{2}xdx
integral of (3x-2/x)	\int\:(3x-\frac{2}{x})dx
(dy)/(dx)=sqrt(20x+y)-20	\frac{dy}{dx}=\sqrt{20x+y}-20
integral from 7 to infinity of 9/(v^2-v)	\int\:_{7}^{\infty\:}\frac{9}{v^{2}-v}dv
(\partial)/(\partial x)(e^{(x+y)/(x-y)})	\frac{\partial\:}{\partial\:x}(e^{\frac{x+y}{x-y}})
slope of (10.2)(19.14)	slope\:(10.2)(19.14)
limit as x approaches 2+of (\|2-x\|)/(2-x)	\lim\:_{x\to\:2+}(\frac{\left\|2-x\right\|}{2-x})
integral of 8/(9+8x)	\int\:\frac{8}{9+8x}dx
derivative of y=2ln(2x)	derivative\:y=2\ln(2x)
integral of 1/2 y	\int\:\frac{1}{2}ydy
(\partial)/(\partial x)(1/(sqrt(x^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x^{2}}})
2x^2y^{''}+xy^'-y=0	2x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=0
normal of y=x^4+3e^x,(0,3)	normal\:y=x^{4}+3e^{x},(0,3)
derivative of (x^3-3)/(x^2+2)	derivative\:\frac{x^{3}-3}{x^{2}+2}
integral from 1 to 5 of x	\int\:_{1}^{5}xdx
integral of x^2(ln(x))^2	\int\:x^{2}(\ln(x))^{2}dx
(\partial)/(\partial x)(e^{-(x-3)^2})	\frac{\partial\:}{\partial\:x}(e^{-(x-3)^{2}})
d/(dy)(1/8 y^4+1/(4y^2))	\frac{d}{dy}(\frac{1}{8}y^{4}+\frac{1}{4y^{2}})
area y=x^2+1/2 ,(-7,7)	area\:y=x^{2}+\frac{1}{2},(-7,7)
derivative of y=-6x	derivative\:y=-6x
integral of (2/(x^3)+sqrt(x^4))	\int\:(\frac{2}{x^{3}}+\sqrt{x^{4}})dx
derivative of ln(tan(2x))	\frac{d}{dx}(\ln(\tan(2x)))
(\partial)/(\partial t)(1-cos(t))	\frac{\partial\:}{\partial\:t}(1-\cos(t))
derivative of 8/(x^7)	\frac{d}{dx}(\frac{8}{x^{7}})
integral of (x^2+4x+1)/(x+3)	\int\:\frac{x^{2}+4x+1}{x+3}dx
integral from 0 to 1 of t^3(1+t^4)^3	\int\:_{0}^{1}t^{3}(1+t^{4})^{3}dt
(dy)/(dx)=-10x^4+8x^3	\frac{dy}{dx}=-10x^{4}+8x^{3}
tangent of f(x)=7x-sqrt(x),(4,26)	tangent\:f(x)=7x-\sqrt{x},(4,26)
derivative of f(x)=((x+11)/(x-11))^6	derivative\:f(x)=(\frac{x+11}{x-11})^{6}
integral of x^3e^{4x^2}	\int\:x^{3}e^{4x^{2}}dx
derivative of (2sin(x)/(sec(x)))	\frac{d}{dx}(\frac{2\sin(x)}{\sec(x)})
inverse oflaplace 2/((s-4)^2)	inverselaplace\:\frac{2}{(s-4)^{2}}
tangent of f(x)= 7/x ,7,\at x=5	tangent\:f(x)=\frac{7}{x},7,\at\:x=5
integral from 0 to 4 of 2pixsqrt(x)	\int\:_{0}^{4}2πx\sqrt{x}dx
derivative of 1/(1+e^{1/x})	\frac{d}{dx}(\frac{1}{1+e^{\frac{1}{x}}})
integral of (50)/((x+1)(x^2+9)^2)	\int\:\frac{50}{(x+1)(x^{2}+9)^{2}}dx
derivative of (dy/(dx))+k^2y=ae^{-bx}	\frac{d}{dx}(\frac{dy}{dx})+k^{2}y=ae^{-bx}
inverse oflaplace 2/(s+8)	inverselaplace\:\frac{2}{s+8}
slope of (-4,2),(-1,-5)	slope\:(-4,2),(-1,-5)
limit as x approaches 3-of (\|x\|)/x	\lim\:_{x\to\:3-}(\frac{\left\|x\right\|}{x})
integral of 5x-4	\int\:5x-4dx
integral of xln(x+4)	\int\:x\ln(x+4)dx
integral of ln(y)+2xy^3	\int\:\ln(y)+2xy^{3}dx
-xy+(3+x)((dy)/(dx))=0	-xy+(3+x)(\frac{dy}{dx})=0
integral from 0 to 1/2 of 2arccos(x)	\int\:_{0}^{\frac{1}{2}}2\arccos(x)dx
integral of (20)/(x^{-1)+5}	\int\:\frac{20}{x^{-1}+5}dx
(\partial)/(\partial x)(2xy^{-1})	\frac{\partial\:}{\partial\:x}(2xy^{-1})
sum from n=1 to infinity of 8(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}8(0.8)^{n-1}
integral of 105e^{0.05t}	\int\:105e^{0.05t}dt
integral of 1/(sqrt(3x-4))	\int\:\frac{1}{\sqrt{3x-4}}dx
integral of (5x^2-3x+2)/(x^3-2x^2)	\int\:\frac{5x^{2}-3x+2}{x^{3}-2x^{2}}dx
limit as x approaches 3 of x^2-5	\lim\:_{x\to\:3}(x^{2}-5)
y^'=(y+sqrt(x^2-y^2))/x	y^{\prime\:}=\frac{y+\sqrt{x^{2}-y^{2}}}{x}
integral from-2.5 to 4.5 of x^3	\int\:_{-2.5}^{4.5}x^{3}dx
derivative of acos(x)	\frac{d}{dx}(a\cos(x))
limit as x approaches-1 of sqrt(5-3x)	\lim\:_{x\to\:-1}(\sqrt{5-3x})
tangent of y=sqrt(5x+1)	tangent\:y=\sqrt{5x+1}
sum from n=0 to infinity of (x/5)^n	\sum\:_{n=0}^{\infty\:}(\frac{x}{5})^{n}
integral of x/(sqrt(x^2+y^2+z^2))	\int\:\frac{x}{\sqrt{x^{2}+y^{2}+z^{2}}}dx
limit as x approaches 0 of (sin(12x))/x	\lim\:_{x\to\:0}(\frac{\sin(12x)}{x})
derivative of (x-1/x+ln(x))	\frac{d}{dx}(\frac{x-1}{x}+\ln(x))
laplacetransform 4sin(4t)	laplacetransform\:4\sin(4t)
dy=xsqrt(y)dx	dy=x\sqrt{y}dx
derivative of x-5	derivative\:x-5
integral of 8/((x+2)(x^2+4))	\int\:\frac{8}{(x+2)(x^{2}+4)}dx
(\partial)/(\partial x)(cos(xy)+sin(yz))	\frac{\partial\:}{\partial\:x}(\cos(xy)+\sin(yz))
derivative of (8x/(9-tan(x)))	\frac{d}{dx}(\frac{8x}{9-\tan(x)})
tangent of (-5x^2)/(2x+3)	tangent\:\frac{-5x^{2}}{2x+3}
integral of sec^{-2}(xta)n^3x	\int\:\sec^{-2}(xta)n^{3}xdx
integral from 1 to 7 of pi(x-1)	\int\:_{1}^{7}π(x-1)dx
derivative of arcsin(a/x)	\frac{d}{dx}(\arcsin(\frac{a}{x}))
integral of (x^3-2x^2+5x-2)/(x^3-2x^2+x)	\int\:\frac{x^{3}-2x^{2}+5x-2}{x^{3}-2x^{2}+x}dx
derivative of-2sin^2(x)	\frac{d}{dx}(-2\sin^{2}(x))
derivative of 4x^2+x+1	\frac{d}{dx}(4x^{2}+x+1)
sum from n=1 to infinity of ((ln(3n)))/n	\sum\:_{n=1}^{\infty\:}\frac{(\ln(3n))}{n}
derivative of (2x^3+3)^6	derivative\:(2x^{3}+3)^{6}
derivative of (2x-3)^6	derivative\:(2x-3)^{6}
expand \sqrt[3]{x}(2+x)	expand\:\sqrt[3]{x}(2+x)
limit as x approaches 0+of e^{cot(x)}	\lim\:_{x\to\:0+}(e^{\cot(x)})
(dy}{dx}= y/x+\frac{y^2)/x	\frac{dy}{dx}=\frac{y}{x}+\frac{y^{2}}{x}
limit as x approaches 1 of 2x^3	\lim\:_{x\to\:1}(2x^{3})
(y-b)*y^'+x-a=0	(y-b)\cdot\:y^{\prime\:}+x-a=0
integral of sqrt(19-18x-x^2)	\int\:\sqrt{19-18x-x^{2}}dx
(\partial)/(\partial y)(x^3-xy)	\frac{\partial\:}{\partial\:y}(x^{3}-xy)
derivative of f(x)=(-3x^2-2)^4	derivative\:f(x)=(-3x^{2}-2)^{4}
limit as x approaches 0.9 of 2(0.9)+1	\lim\:_{x\to\:0.9}(2(0.9)+1)
limit as x approaches 6 of x^2	\lim\:_{x\to\:6}(x^{2})
slope of (3/10 ,-2),(-1/5 ,-1/5)	slope\:(\frac{3}{10},-2),(-\frac{1}{5},-\frac{1}{5})
limit as x approaches 0 of x/(sin(9x))	\lim\:_{x\to\:0}(\frac{x}{\sin(9x)})
derivative of y=(4x+3)(2x^2+7x-1)	derivative\:y=(4x+3)(2x^{2}+7x-1)
integral from 0 to 1/7 of xarcsin(7x)	\int\:_{0}^{\frac{1}{7}}x\arcsin(7x)dx
(2dy)/(dx)-4xy=8x,y(0)=15	\frac{2dy}{dx}-4xy=8x,y(0)=15
derivative of ln((1+x^2/(1-x^2)))	\frac{d}{dx}(\ln(\frac{1+x^{2}}{1-x^{2}}))
integral of 1/(sqrt(t^2-10t+29))	\int\:\frac{1}{\sqrt{t^{2}-10t+29}}dt
(d^2y)/(dx^2)=((dy)/(dx))^2	\frac{d^{2}y}{dx^{2}}=(\frac{dy}{dx})^{2}
4y^{''}+7y=0	4y^{\prime\:\prime\:}+7y=0
(\partial)/(\partial x)(-3y)	\frac{\partial\:}{\partial\:x}(-3y)
(\partial)/(\partial x)(e^{2x}-xcos(t))	\frac{\partial\:}{\partial\:x}(e^{2x}-x\cos(t))
5(dy)/(dx)+30y=6	5\frac{dy}{dx}+30y=6

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