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Popular Calculus Problems

integral of-cos(x)+sin(x)+1	\int\:-\cos(x)+\sin(x)+1dx
sum from n=2 to infinity of 5(-1/3)^n	\sum\:_{n=2}^{\infty\:}5(-\frac{1}{3})^{n}
integral of (5x^2)/2	\int\:\frac{5x^{2}}{2}dx
derivative of y=(3ln(4x))/(5-2x)	derivative\:y=\frac{3\ln(4x)}{5-2x}
tangent of f(x)=-3x^3-2x,(-1,5)	tangent\:f(x)=-3x^{3}-2x,(-1,5)
x^2y^'+y=0	x^{2}y^{\prime\:}+y=0
derivative of nlog_{10}(n)	derivative\:n\log_{10}(n)
integral of 1/((x-1)^{2/3)}	\int\:\frac{1}{(x-1)^{\frac{2}{3}}}dx
integral of 9x^2sin(8x)	\int\:9x^{2}\sin(8x)dx
(\partial)/(\partial y)(sqrt(tan(x)+y))	\frac{\partial\:}{\partial\:y}(\sqrt{\tan(x)+y})
derivative of 3+3sin(x)	\frac{d}{dx}(3+3\sin(x))
limit as x approaches 5 of xsqrt(34-x^2)	\lim\:_{x\to\:5}(x\sqrt{34-x^{2}})
integral of 4z	\int\:4zdz
integral of (5x^2+x+6)/(x^3-1)	\int\:\frac{5x^{2}+x+6}{x^{3}-1}dx
(\partial)/(\partial y)(x^{9y})	\frac{\partial\:}{\partial\:y}(x^{9y})
integral of (x^2)/(x^3-x^2+4x-4)	\int\:\frac{x^{2}}{x^{3}-x^{2}+4x-4}dx
integral of xarctan(3x)	\int\:x\arctan(3x)dx
limit as x approaches 0-of (\|x-7\|)/(x-7)	\lim\:_{x\to\:0-}(\frac{\left\|x-7\right\|}{x-7})
y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=8	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0,y(0)=3,y^{\prime\:}(0)=8
derivative of 8sqrt(3x^2+9)	derivative\:8\sqrt{3x^{2}+9}
(\partial)/(\partial x)(42e^{7x}y)	\frac{\partial\:}{\partial\:x}(42e^{7x}y)
tangent of f(x)= x/(x^2+64)	tangent\:f(x)=\frac{x}{x^{2}+64}
integral from 0 to 1 of 2pi(2-y)(4-4y^2)	\int\:_{0}^{1}2π(2-y)(4-4y^{2})dy
area y=-2x+3,(0,1)	area\:y=-2x+3,(0,1)
integral of x^2cos(a)x	\int\:x^{2}\cos(a)xdx
(\partial)/(\partial x)(3xe^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(3xe^{\sqrt{xy}})
area x+1,0,0,8	area\:x+1,0,0,8
integral of sin^5(2x)	\int\:\sin^{5}(2x)dx
integral of cos(4x)cos(3x)	\int\:\cos(4x)\cos(3x)dx
integral of sqrt(16x^2-1)	\int\:\sqrt{16x^{2}-1}dx
integral of 1/(vln(v))	\int\:\frac{1}{v\ln(v)}dv
area y=3sin(x),y=e^{7x},x=0,x= pi/2	area\:y=3\sin(x),y=e^{7x},x=0,x=\frac{π}{2}
(\partial)/(\partial x)(y^5sin(3x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(3x))
integral from 0 to 2 of 6^x	\int\:_{0}^{2}6^{x}dx
limit as x approaches 0 of 9/x-9/(x^2+x)	\lim\:_{x\to\:0}(\frac{9}{x}-\frac{9}{x^{2}+x})
limit as x approaches 1 of (2x-2)/(x-1)	\lim\:_{x\to\:1}(\frac{2x-2}{x-1})
integral from 1 to 2 of (xsqrt(x-1))	\int\:_{1}^{2}(x\sqrt{x-1})dx
integral from 0 to 5 of sqrt(1+x)	\int\:_{0}^{5}\sqrt{1+x}dx
integral of 1/(sqrt(x^2+8x+25))	\int\:\frac{1}{\sqrt{x^{2}+8x+25}}dx
d/(d{x)}({y}^2sin({x}{z}))	\frac{d}{d{x}}({y}^{2}\sin({x}{z}))
integral of 6sec^3(x)	\int\:6\sec^{3}(x)dx
derivative of 2/(x-11)	\frac{d}{dx}(\frac{2}{x-11})
limit as x approaches 9 of 6/((x-9)^2)	\lim\:_{x\to\:9}(\frac{6}{(x-9)^{2}})
limit as x approaches 0 of x/(x+x^2)	\lim\:_{x\to\:0}(\frac{x}{x+x^{2}})
limit as x approaches 0 of 3x-2	\lim\:_{x\to\:0}(3x-2)
integral of xsqrt(x+5)	\int\:x\sqrt{x+5}dx
limit as x approaches 0 of (tanh(x))/x	\lim\:_{x\to\:0}(\frac{\tanh(x)}{x})
derivative of 1/3 tan(x)	\frac{d}{dx}(\frac{1}{3}\tan(x))
laplacetransform 0.5e^{-4.5t}sin(2pit)	laplacetransform\:0.5e^{-4.5t}\sin(2πt)
(dy)/(dx)=3x-y+4	\frac{dy}{dx}=3x-y+4
integral of ((ln(x))^{50})/x	\int\:\frac{(\ln(x))^{50}}{x}dx
laplacetransform s^2	laplacetransform\:s^{2}
(x/(x^2+1))^'	(\frac{x}{x^{2}+1})^{\prime\:}
integral of cos(x)sin(x)e^{-2cos(x)}	\int\:\cos(x)\sin(x)e^{-2\cos(x)}dx
y^'=2x(x-4)	y^{\prime\:}=2x(x-4)
limit as x approaches pi+of csc(x)	\lim\:_{x\to\:π+}(\csc(x))
integral of tan^2(t)	\int\:\tan^{2}(t)dt
integral of (x^3+93x+70)/(x^3+100x)	\int\:\frac{x^{3}+93x+70}{x^{3}+100x}dx
derivative of y=x^3-(x^2)/(16)+4x+5	derivative\:y=x^{3}-\frac{x^{2}}{16}+4x+5
tangent of f(x)=2x^2+3x-2,\at x=-1	tangent\:f(x)=2x^{2}+3x-2,\at\:x=-1
derivative of k(1-w/d e^{-sx}sin(dx+t))	\frac{d}{dx}(k(1-\frac{w}{d}e^{-sx}\sin(dx+t)))
laplacetransform-x	laplacetransform\:-x
derivative of (sqrt(9-x^2))/(16x)	derivative\:\frac{\sqrt{9-x^{2}}}{16x}
integral of pix	\int\:πxdx
derivative of in^2(x+3)	\frac{d}{dx}(in^{2}(x+3))
integral from 0 to 4 of sqrt(2x+1)	\int\:_{0}^{4}\sqrt{2x+1}dx
limit as x approaches 3+of 6/((x-3)^5)	\lim\:_{x\to\:3+}(\frac{6}{(x-3)^{5}})
derivative of y= 4/(x^4)	derivative\:y=\frac{4}{x^{4}}
(x+2)^'	(x+2)^{\prime\:}
derivative of f(x)=(2x^3+3x)(x-3)(x+5)	derivative\:f(x)=(2x^{3}+3x)(x-3)(x+5)
y^{''}-8y^'+20y=100x^2-26xe^x	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=100x^{2}-26xe^{x}
integral of-x+2	\int\:-x+2dx
derivative of 16ln(x)	\frac{d}{dx}(16\ln(x))
integral of x/((x^2+2)^{3/2)}	\int\:\frac{x}{(x^{2}+d^{2})^{\frac{3}{2}}}dx
y^{''}-3y^'+2y=14sin(2x)-18cos(2x)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=14\sin(2x)-18\cos(2x)
derivative of x+sin(y)	\frac{d}{dx}(x+\sin(y))
integral of (9x^3-6x+4)/(x^3-x^2)	\int\:\frac{9x^{3}-6x+4}{x^{3}-x^{2}}dx
(\partial)/(\partial t)(e^{-2t}cos(2x))	\frac{\partial\:}{\partial\:t}(e^{-2t}\cos(2x))
integral of (2e^{3x})	\int\:(2e^{3x})dx
integral of (4x^2+1/((4x)^2))	\int\:(4x^{2}+\frac{1}{(4x)^{2}})dx
y^'=9xsqrt(7y+8),y(0)=3	y^{\prime\:}=9x\sqrt{7y+8},y(0)=3
derivative of (x*cos(x+pi)/(pi-x))	\frac{d}{dx}(\frac{x\cdot\:\cos(x)+π}{π-x})
derivative of t/3	derivative\:\frac{t}{3}
integral of r^3sqrt(1+4r^2)	\int\:r^{3}\sqrt{1+4r^{2}}dr
derivative of 1/(3(1+e^{-t))^3}	derivative\:\frac{1}{3(1+e^{-t})^{3}}
xdy+3ydx=xydy	xdy+3ydx=xydy
derivative of y=\sqrt[3]{t}+6sqrt(t^3)	derivative\:y=\sqrt[3]{t}+6\sqrt{t^{3}}
limit as x approaches+0 of (-6)/(x^7)	\lim\:_{x\to\:+0}(\frac{-6}{x^{7}})
integral from 0 to 3 of \|x-2\|	\int\:_{0}^{3}\left\|x-2\right\|dx
integral of 1/(x^2-2x+65)	\int\:\frac{1}{x^{2}-2x+65}dx
tangent of f(x)=x^2+3x,\at x=-2	tangent\:f(x)=x^{2}+3x,\at\:x=-2
derivative of sqrt(((z-1))/(z+1))	derivative\:\sqrt{\frac{(z-1)}{z+1}}
integral of (6x-1)/(4x^2+4x+10)	\int\:\frac{6x-1}{4x^{2}+4x+10}dx
integral of (28)/((196x^2+1)^2)	\int\:\frac{28}{(196x^{2}+1)^{2}}dx
(\partial)/(\partial y)(-4e^xcos(yz))	\frac{\partial\:}{\partial\:y}(-4e^{x}\cos(yz))
derivative of sqrt(1+x^2)+x^2sqrt(1+x^2)	\frac{d}{dx}(\sqrt{1+x^{2}}+x^{2}\sqrt{1+x^{2}})
integral of (5e^{2x}+1/x)	\int\:(5e^{2x}+\frac{1}{x})dx
derivative of sin(kt)	\frac{d}{dx}(\sin(kt))
derivative of f(x)=(5+2x)e^{-3x}	derivative\:f(x)=(5+2x)e^{-3x}
derivative of 2*e^{2x}	\frac{d}{dx}(2\cdot\:e^{2x})

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