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Popular Calculus Problems

tangent of f(x)=(3+4x^{1/2})/(2+x^{3/2)}	tangent\:f(x)=\frac{3+4x^{\frac{1}{2}}}{2+x^{\frac{3}{2}}}
integral of (x^2)/((sqrt(5-x^2))^3)	\int\:\frac{x^{2}}{(\sqrt{5-x^{2}})^{3}}dx
sum from n=0 to infinity of cos(pin)	\sum\:_{n=0}^{\infty\:}\cos(πn)
derivative of ln(x^3-2x^2+2)	\frac{d}{dx}(\ln(x^{3}-2x^{2}+2))
integral of sec^4(x)tan^4(x)	\int\:\sec^{4}(x)\tan^{4}(x)dx
derivative of f(x)=(x^3+7x^2+5)^5	derivative\:f(x)=(x^{3}+7x^{2}+5)^{5}
derivative of (x+1^{-1/2})	\frac{d}{dx}((x+1)^{-\frac{1}{2}})
derivative of cos(e^{x^2})	\frac{d}{dx}(\cos(e^{x^{2}}))
integral of (sin(x))/(2x)	\int\:\frac{\sin(x)}{2x}dx
parity ,sqrt(x)	parity\:,\sqrt{x}
derivative of f(1)=9+3/x	derivative\:f(1)=9+\frac{3}{x}
derivative of f(x)=sqrt(3x+8)	derivative\:f(x)=\sqrt{3x+8}
derivative of (4-x^2/(3x-2))	\frac{d}{dx}(\frac{4-x^{2}}{3x-2})
y^'=(-1)/(x^2)	y^{\prime\:}=\frac{-1}{x^{2}}
sum from n=0 to infinity of 1/5*(-2/3)^n	\sum\:_{n=0}^{\infty\:}\frac{1}{5}\cdot\:(-\frac{2}{3})^{n}
tangent of x^2+y^2=25,(-4,3)	tangent\:x^{2}+y^{2}=25,(-4,3)
limit as x approaches 0+of cos(pi/x)	\lim\:_{x\to\:0+}(\cos(\frac{π}{x}))
derivative of (1+x^{1/3})	\frac{d}{dx}((1+x)^{\frac{1}{3}})
limit as x approaches x of (x^2-1)/(x-1)	\lim\:_{x\to\:x}(\frac{x^{2}-1}{x-1})
derivative of y=sin(x^3)	derivative\:y=\sin(x^{3})
integral of (x^3-x)/(x^3)	\int\:\frac{x^{3}-x}{x^{3}}dx
sum from n=0 to infinity of (-1+1/e)^n	\sum\:_{n=0}^{\infty\:}(-1+\frac{1}{e})^{n}
d/(dθ)(3sin(3θ))	\frac{d}{dθ}(3\sin(3θ))
slope of m 7/(sqrt(x))	slope\:m\frac{7}{\sqrt{x}}
derivative of f(x)=sqrt(2+\sqrt{7x)}	derivative\:f(x)=\sqrt{2+\sqrt{7x}}
inverse oflaplace 8/((s+1)^2)	inverselaplace\:\frac{8}{(s+1)^{2}}
(d^2x)/(dt^2)+(dx)/(dt)+x=0.5sin(2t)	\frac{d^{2}x}{dt^{2}}+\frac{dx}{dt}+x=0.5\sin(2t)
integral of 1/(sqrt(x^2-25))	\int\:\frac{1}{\sqrt{x^{2}-25}}dx
integral of (3/(x^2))	\int\:(\frac{3}{x^{2}})dx
integral of 2/3 x^2ln(x)	\int\:\frac{2}{3}x^{2}\ln(x)dx
limit as x approaches 1 of ((x^2-5))/x	\lim\:_{x\to\:1}(\frac{(x^{2}-5)}{x})
limit as x approaches 5 of sqrt(8x+5)	\lim\:_{x\to\:5}(\sqrt{8x+5})
derivative of e^{x^2y}-2x-2y	\frac{d}{dx}(e^{x^{2}y}-2x-2y)
integral of x^3e^{12x}	\int\:x^{3}e^{12x}dx
derivative of (x^4+3x^{-1})	\frac{d}{dx}((x^{4}+3x)^{-1})
inverse oflaplace (s-1)/((s+1)(s+2)s)	inverselaplace\:\frac{s-1}{(s+1)(s+2)s}
f(x)= 5/(x^5)	f(x)=\frac{5}{x^{5}}
taylor f(x)=sin(x),0	taylor\:f(x)=\sin(x),0
area x^2+x+3,[1,3]	area\:x^{2}+x+3,[1,3]
integral of 2/3 cos^2(3x)	\int\:\frac{2}{3}\cos^{2}(3x)dx
maclaurin 1/(1+4x^2)	maclaurin\:\frac{1}{1+4x^{2}}
derivative of f(x)=e^x-cot(x)	derivative\:f(x)=e^{x}-\cot(x)
derivative of xsin(x^3)	\frac{d}{dx}(x\sin(x^{3}))
integral from-1 to 5 of (y^2-5)-4y	\int\:_{-1}^{5}(y^{2}-5)-4ydy
integral from 0 to 2 of 20000e^{0.03x}	\int\:_{0}^{2}20000e^{0.03x}dx
sum from k=1 to infinity of k*2^{-k}	\sum\:_{k=1}^{\infty\:}k\cdot\:2^{-k}
limit as h approaches 0 of-8p-4h-7	\lim\:_{h\to\:0}(-8p-4h-7)
limit as x approaches 0 of (e^x+x)^{8/x}	\lim\:_{x\to\:0}((e^{x}+x)^{\frac{8}{x}})
integral of 1/(xsqrt(1+ln(x)))	\int\:\frac{1}{x\sqrt{1+\ln(x)}}dx
integral from 0 to pi/2 of sin(t)	\int\:_{0}^{\frac{π}{2}}\sin(t)dt
derivative of (e^x/(4x))	\frac{d}{dx}(\frac{e^{x}}{4x})
integral from 0 to 4 of (2sqrt(x))^2	\int\:_{0}^{4}(2\sqrt{x})^{2}dx
area sqrt(9x),1,9	area\:\sqrt{9x},1,9
(\partial)/(\partial x)(sin^8(x-4y))	\frac{\partial\:}{\partial\:x}(\sin^{8}(x-4y))
limit as x approaches 1 of (sqrt(10x-9)-1)/(x-1)	\lim\:_{x\to\:1}(\frac{\sqrt{10x-9}-1}{x-1})
derivative of ln(3x+4)	\frac{d}{dx}(\ln(3x+4))
derivative of ln(t^2+6)	derivative\:\ln(t^{2}+6)
derivative of t^2e^t	derivative\:t^{2}e^{t}
(\partial)/(\partial x)(sin(4y)e^{-5x})	\frac{\partial\:}{\partial\:x}(\sin(4y)e^{-5x})
f(x)=-x^3-150x^2+60000x-800	f(x)=-x^{3}-150x^{2}+60000x-800
integral of e^x(sin(x)+cos(x))	\int\:e^{x}(\sin(x)+\cos(x))dx
(\partial)/(\partial y)(x-4y-9)	\frac{\partial\:}{\partial\:y}(x-4y-9)
integral of (4+3x)^4	\int\:(4+3x)^{4}dx
derivative of cos(x^{-9})	derivative\:\cos(x^{-9})
derivative of 3-7/(2x^{1/8})	\frac{d}{dx}(3-\frac{7}{2x^{\frac{1}{8}}})
area x^2+y^2=4,x^2+y^2=4x	area\:x^{2}+y^{2}=4,x^{2}+y^{2}=4x
d/(dy)((y^{3/2})/5)	\frac{d}{dy}(\frac{y^{\frac{3}{2}}}{5})
integral of ((x^2+1-2x)^{1/5})/(1-x)	\int\:\frac{(x^{2}+1-2x)^{\frac{1}{5}}}{1-x}dx
integral of (x^6)/(sqrt(1-x^{14))}	\int\:\frac{x^{6}}{\sqrt{1-x^{14}}}dx
integral of 3cot^4(x)	\int\:3\cot^{4}(x)dx
derivative of 5x-1	\frac{d}{dx}(5x-1)
tangent of f(x)=x^2-3x,\at x=1	tangent\:f(x)=x^{2}-3x,\at\:x=1
integral of (12-3t^2)	\int\:(12-3t^{2})dt
inverse oflaplace (2s)/((s+3)^2+7)	inverselaplace\:\frac{2s}{(s+3)^{2}+7}
limit as x approaches-2 of (x+1)*(x+1)	\lim\:_{x\to\:-2}((x+1)\cdot\:(x+1))
integral of sqrt(7x+1)	\int\:\sqrt{7x+1}dx
integral of x\sqrt[3]{5-6x^2}	\int\:x\sqrt[3]{5-6x^{2}}dx
(\partial)/(\partial y)(tan(2x+y))	\frac{\partial\:}{\partial\:y}(\tan(2x+y))
0=2x+1-2yy^'	0=2x+1-2yy^{\prime\:}
integral of sqrt(2[1-cos^2(\sqrt{2)x)]}	\int\:\sqrt{2[1-\cos^{2}(\sqrt{2}x)]}dx
integral of cos(x)(2+sin(x))^6	\int\:\cos(x)(2+\sin(x))^{6}dx
(dy)/(dt)+ty^2=0	\frac{dy}{dt}+ty^{2}=0
derivative of (4x)/(e^x)	derivative\:\frac{4x}{e^{x}}
derivative of (1+1/x)	\frac{d}{dx}(\frac{1+1}{x})
area 1-x^2,\|x\|	area\:1-x^{2},\left\|x\right\|
derivative of \sqrt[4]{1+x}	\frac{d}{dx}(\sqrt[4]{1+x})
integral of sin^{100}(x)cos^3(x)	\int\:\sin^{100}(x)\cos^{3}(x)dx
(\partial)/(\partial x)(ln(x+7y+9z))	\frac{\partial\:}{\partial\:x}(\ln(x+7y+9z))
limit as x approaches 0 of (2x-sin(x))/x	\lim\:_{x\to\:0}(\frac{2x-\sin(x)}{x})
integral of (7-2x)/(x^{1/2)}	\int\:\frac{7-2x}{x^{\frac{1}{2}}}dx
derivative of 1/((a^2+x^2^{n/2)})	\frac{d}{dx}(\frac{1}{(a^{2}+x^{2})^{\frac{n}{2}}})
integral of t^3ln(t)	\int\:t^{3}\ln(t)dt
integral of sin(mx)sin(nx)	\int\:\sin(mx)\sin(nx)dx
derivative of y=(8x^2+2x+6)/(sqrt(x))	derivative\:y=\frac{8x^{2}+2x+6}{\sqrt{x}}
derivative of 1000xe^{-0.5x}	\frac{d}{dx}(1000xe^{-0.5x})
(\partial)/(\partial x)(z^3ln(xy))	\frac{\partial\:}{\partial\:x}(z^{3}\ln(xy))
derivative of f(x)=-2x^2-5x+2	derivative\:f(x)=-2x^{2}-5x+2
integral from 0 to 2 of 4^{-θ}	\int\:_{0}^{2}4^{-θ}dθ
integral of (3x^2-1)	\int\:(3x^{2}-1)dx
derivative of f(x)=2x^3+4x^2+6x	derivative\:f(x)=2x^{3}+4x^{2}+6x

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