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Popular Calculus Problems

integral of 1/((1+x^2)x)	\int\:\frac{1}{(1+x^{2})x}dx
sin(y)(dy)/(dx)-cos(y)=0	\sin(y)\frac{dy}{dx}-\cos(y)=0
derivative of (x-3/2)	\frac{d}{dx}(\frac{x-3}{2})
integral of 6x^5-4x^4-9x^2	\int\:6x^{5}-4x^{4}-9x^{2}dx
integral of (2x^3-9x^2+5x)e^{-x}	\int\:(2x^{3}-9x^{2}+5x)e^{-x}dx
integral of x/(2(x^2+1))	\int\:\frac{x}{2(x^{2}+1)}dx
derivative of (e^x+e^{-x}/(x^3))	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{x^{3}})
y^3-(14x+8)+3xy^2(dy)/(dx)=0	y^{3}-(14x+8)+3xy^{2}\frac{dy}{dx}=0
(\partial)/(\partial y)(sin(xy)+e^{xy})	\frac{\partial\:}{\partial\:y}(\sin(xy)+e^{xy})
integral from-7 to 7 of y/(sqrt(49-y^2))	\int\:_{-7}^{7}\frac{y}{\sqrt{49-y^{2}}}dy
derivative of 4arcsin(x^3)	derivative\:4\arcsin(x^{3})
integral from 0 to 2 of (xsqrt(9-x^2))	\int\:_{0}^{2}(x\sqrt{9-x^{2}})dx
integral of (3x-5)^2	\int\:(3x-5)^{2}dx
sum from n=1 to infinity of 1/(n^{1.1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{1.1}}
integral of 7/(6+7x)	\int\:\frac{7}{6+7x}dx
limit as x approaches 9 of (x+9)/(x-9)	\lim\:_{x\to\:9}(\frac{x+9}{x-9})
derivative of sin(sqrt(ln(1-3x)))	\frac{d}{dx}(\sin(\sqrt{\ln(1-3x)}))
d/(dt)((dx)/(dt))+x=sin(2t)	\frac{d}{dt}(\frac{dx}{dt})+x=\sin(2t)
integral from 0 to infinity of 8sin^2(a)	\int\:_{0}^{\infty\:}8\sin^{2}(a)da
y^{''}-10y^'+25y=e^{5x}	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=e^{5x}
integral from 0 to 2 of sqrt(144x+289)	\int\:_{0}^{2}\sqrt{144x+289}dx
derivative of 16\sqrt[4]{4x^4+4}	derivative\:16\sqrt[4]{4x^{4}+4}
derivative of t^3-1/(\sqrt[4]{t^7)}	derivative\:t^{3}-\frac{1}{\sqrt[4]{t^{7}}}
tangent of f(x)= 1/(x-1),\at x=2	tangent\:f(x)=\frac{1}{x-1},\at\:x=2
inverse oflaplace 1/(s(s+8))	inverselaplace\:\frac{1}{s(s+8)}
integral of x^x(1+ln(x))	\int\:x^{x}(1+\ln(x))dx
derivative of (x^4+9)/(x^2)	derivative\:\frac{x^{4}+9}{x^{2}}
(dx)/(dt)=2(2xt)	\frac{dx}{dt}=2(2xt)
integral from-1 to 8 of 2-\sqrt[3]{x}	\int\:_{-1}^{8}2-\sqrt[3]{x}dx
limit as x approaches-1+of 1/((x+1)^2)	\lim\:_{x\to\:-1+}(\frac{1}{(x+1)^{2}})
integral of (4sqrt(x))/(sqrt(4x+1))	\int\:\frac{4\sqrt{x}}{\sqrt{4x+1}}dx
derivative of 9cos^2(t)	derivative\:9\cos^{2}(t)
derivative of x^3-1	derivative\:x^{3}-1
(\partial)/(\partial x)(e^y+x+x^2+5)	\frac{\partial\:}{\partial\:x}(e^{y}+x+x^{2}+5)
(\partial)/(\partial x)((2y)/(x^2+2))	\frac{\partial\:}{\partial\:x}(\frac{2y}{x^{2}+2})
derivative of y=\sqrt[3]{t}+4sqrt(t^3)	derivative\:y=\sqrt[3]{t}+4\sqrt{t^{3}}
integral of x/((4x^2+3)^2)	\int\:\frac{x}{(4x^{2}+3)^{2}}dx
integral of cos(2x)cos(4x)	\int\:\cos(2x)\cos(4x)dx
derivative of {f}(h,x{g}(h,x)h)	\frac{d}{dx}({f}(h,x)\cdot\:{g}(h,x)\cdot\:h)
derivative of 1/(sqrt(5x))	\frac{d}{dx}(\frac{1}{\sqrt{5x}})
integral of (sin(x)sqrt(x))/(sqrt(x))	\int\:\frac{\sin(x)\sqrt{x}}{\sqrt{x}}dx
derivative of (3x^2+3)(2x^2+1)	derivative\:(3x^{2}+3)(2x^{2}+1)
integral of-y/(x^2+y^2)	\int\:-\frac{y}{x^{2}+y^{2}}dx
limit as x approaches 2 of x^3-8	\lim\:_{x\to\:2}(x^{3}-8)
y^'(t)=(y+1)(y-1),y(0)=3	y^{\prime\:}(t)=(y+1)(y-1),y(0)=3
implicit (dy)/(dx),(2x+3)^4=3y^4	implicit\:\frac{dy}{dx},(2x+3)^{4}=3y^{4}
derivative of f(x)=5x^2-2x+5	derivative\:f(x)=5x^{2}-2x+5
taylor cos(x^2)	taylor\:\cos(x^{2})
(\partial)/(\partial u)(u^2+v^2-4)	\frac{\partial\:}{\partial\:u}(u^{2}+v^{2}-4)
integral of x*(sqrt(x^2-3))	\int\:x\cdot\:(\sqrt{x^{2}-3})dx
derivative of y=xsin(1/x)	derivative\:y=x\sin(\frac{1}{x})
derivative of 3x^2(x^3+1)^7	derivative\:3x^{2}(x^{3}+1)^{7}
limit as x approaches 0 of (sin^2(4x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(4x)}{x})
limit as x approaches 0+of-1/(sin(2x))	\lim\:_{x\to\:0+}(-\frac{1}{\sin(2x)})
laplacetransform 4(t+3)	laplacetransform\:4(t+3)
derivative of yx^{y-1}	\frac{d}{dx}(yx^{y-1})
integral of (2sin(x)cos(x))/(1+tan(x))	\int\:\frac{2\sin(x)\cos(x)}{1+\tan(x)}dx
y^{''}+y^'=1	y^{\prime\:\prime\:}+y^{\prime\:}=1
integral from 0 to 1 of (e^{1/x})/(x^3)	\int\:_{0}^{1}\frac{e^{\frac{1}{x}}}{x^{3}}dx
slope of (0,2.5),(0.833,0)	slope\:(0,2.5),(0.833,0)
tangent of f(x)=2x^3-2x,\at x=-1	tangent\:f(x)=2x^{3}-2x,\at\:x=-1
(\partial)/(\partial y)(sin(x+2y))	\frac{\partial\:}{\partial\:y}(\sin(x+2y))
integral from 0 to pi of 2pixsin(x)	\int\:_{0}^{π}2πx\sin(x)dx
(\partial)/(\partial x)((xy)^5)	\frac{\partial\:}{\partial\:x}((xy)^{5})
derivative of x^2*In(x)	\frac{d}{dx}(x^{2}\cdot\:In(x))
tangent of f(x)=(1+2x)(6-5x),\at x=1	tangent\:f(x)=(1+2x)(6-5x),\at\:x=1
(\partial)/(\partial x)(2ln(xy))	\frac{\partial\:}{\partial\:x}(2\ln(xy))
integral of ((ln(x))^{28})/x	\int\:\frac{(\ln(x))^{28}}{x}dx
derivative of arcsin(3x+1)	\frac{d}{dx}(\arcsin(3x+1))
derivative of f(x)=x+3+4/x	derivative\:f(x)=x+3+\frac{4}{x}
d/(dt)(-1)	\frac{d}{dt}(-1)
inverse oflaplace 1/((s+1)^2(s^2+4))	inverselaplace\:\frac{1}{(s+1)^{2}(s^{2}+4)}
area y=sqrt(x+2),y= 1/(x+1),x=2	area\:y=\sqrt{x+2},y=\frac{1}{x+1},x=2
derivative of 2cot(x)	\frac{d}{dx}(2\cot(x))
(\partial)/(\partial x)(2x^2-2xy^2)	\frac{\partial\:}{\partial\:x}(2x^{2}-2xy^{2})
integral of sqrt((x+3)/(x-1))	\int\:\sqrt{\frac{x+3}{x-1}}dx
derivative of arcsin(x/pi)	\frac{d}{dx}(\arcsin(\frac{x}{π}))
integral from 0 to 4 of x^2+1	\int\:_{0}^{4}x^{2}+1dx
inverse oflaplace (1+s2)/((1+s3)^2)	inverselaplace\:\frac{1+s\cdot\:2}{(1+s\cdot\:3)^{2}}
d/(dy)(y/(x^2+y^2))	\frac{d}{dy}(\frac{y}{x^{2}+y^{2}})
integral of (3x^2)/((x^3+1)^5)	\int\:\frac{3x^{2}}{(x^{3}+1)^{5}}dx
derivative of x/((2x-1^6))	\frac{d}{dx}(\frac{x}{(2x-1)^{6}})
integral of (4x+3)^3	\int\:(4x+3)^{3}dx
f(x)=e^{x^2}*2x	f(x)=e^{x^{2}}\cdot\:2x
integral of 5x^3sqrt(1-x^2)	\int\:5x^{3}\sqrt{1-x^{2}}dx
(\partial)/(\partial x)(2x^2-4xy+xyz)	\frac{\partial\:}{\partial\:x}(2x^{2}-4xy+xyz)
(\partial)/(\partial x)(((x(y+3)))/(x^2+y))	\frac{\partial\:}{\partial\:x}(\frac{(x(y+3))}{x^{2}+y})
x^4e^y+(x+1)y(dy)/(dx)=0	x^{4}e^{y}+(x+1)y\frac{dy}{dx}=0
derivative of f(x)=(1+cos^2(x))^6	derivative\:f(x)=(1+\cos^{2}(x))^{6}
integral from 5 to 10 of ax-10b	\int\:_{5}^{10}ax-10bdx
tangent of f(x)=(12)/x ,\at x=-2	tangent\:f(x)=\frac{12}{x},\at\:x=-2
d/(dz)(0)	\frac{d}{dz}(0)
limit as x approaches 0 of 1/(x^{1/2)}	\lim\:_{x\to\:0}(\frac{1}{x^{\frac{1}{2}}})
y^{''}+2y+8=0	y^{\prime\:\prime\:}+2y+8=0
integral of-1/(u^2)	\int\:-\frac{1}{u^{2}}du
(\partial)/(\partial y)((-y^2)/((x-y)^2))	\frac{\partial\:}{\partial\:y}(\frac{-y^{2}}{(x-y)^{2}})
integral of (sqrt(x))^2	\int\:(\sqrt{x})^{2}dx
integral of 1/(xln(x)(ln(ln(x)))^2)	\int\:\frac{1}{x\ln(x)(\ln(\ln(x)))^{2}}dx
(1+x^2+y^2+x^2y^2)dy=(1+y^2)dx	(1+x^{2}+y^{2}+x^{2}y^{2})dy=(1+y^{2})dx
integral of (100)/(100-y)	\int\:\frac{100}{100-y}dy

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