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Popular Calculus Problems

integral of x3^x	\int\:x3^{x}dx
derivative of (csc(x)/(cot(x)))	\frac{d}{dx}(\frac{\csc(x)}{\cot(x)})
integral of (2x^4-8x^3-6x^2+4)/(x^3)	\int\:\frac{2x^{4}-8x^{3}-6x^{2}+4}{x^{3}}dx
y^{''}-4y^'+4y=t^{-5}e^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=t^{-5}e^{2t}
limit as x approaches-8 of x+5	\lim\:_{x\to\:-8}(x+5)
integral of 1/(cos^2(6x))	\int\:\frac{1}{\cos^{2}(6x)}dx
(\partial)/(\partial y)((x^2+y)(x-y^2))	\frac{\partial\:}{\partial\:y}((x^{2}+y)(x-y^{2}))
integral from 0 to 1 of pi(3x)^2	\int\:_{0}^{1}π(3x)^{2}dx
derivative of 7^{sqrt(x)}	\frac{d}{dx}(7^{\sqrt{x}})
y^{''}-y^'+1/4 y=4+e^{x/2}	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=4+e^{\frac{x}{2}}
sum from n=1 to infinity of ((4^n+1))/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{(4^{n}+1)}{5^{n}}
integral of-xe^{-2x}	\int\:-xe^{-2x}dx
derivative of 5-x^2	derivative\:5-x^{2}
taylor cos(pix),\at 1/2	taylor\:\cos(πx),\at\:\frac{1}{2}
derivative of y=ln(3x+1)e^{x^2+4}	derivative\:y=\ln(3x+1)e^{x^{2}+4}
derivative of ((x+7sqrt(x)))/(7x-5)	derivative\:\frac{(x+7\sqrt{x})}{7x-5}
integral of (4x^2-3x+2)/(4x^2-4x+3)	\int\:\frac{4x^{2}-3x+2}{4x^{2}-4x+3}dx
integral from 1 to 2 of (e^{1/x})/(x^2)	\int\:_{1}^{2}\frac{e^{\frac{1}{x}}}{x^{2}}dx
factor 2cos(x)+cos^2(x)	factor\:2\cos(x)+\cos^{2}(x)
integral of sqrt(4+\sqrt{x)}	\int\:\sqrt{4+\sqrt{x}}dx
y^{''}+3y^'+2y=6	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=6
limit as x approaches 6 of 1/(sqrt(x-2))	\lim\:_{x\to\:6}(\frac{1}{\sqrt{x-2}})
area f(x)=cos(x),0,2pi	area\:f(x)=\cos(x),0,2π
tangent of y=-2-7x^2,(-2,-30)	tangent\:y=-2-7x^{2},(-2,-30)
integral of (3cos(x))/(sin^2(x)+sin(x))	\int\:\frac{3\cos(x)}{\sin^{2}(x)+\sin(x)}dx
area x^2-35,5-3x	area\:x^{2}-35,5-3x
sum from n=1 to infinity of 1/n-1/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n}-\frac{1}{n^{2}}
integral from 4 to 7 of x/(x^2-2)	\int\:_{4}^{7}\frac{x}{x^{2}-2}dx
sum from n=3 to infinity of n/(e^{3n)}	\sum\:_{n=3}^{\infty\:}\frac{n}{e^{3n}}
derivative of-cos(x^2)	\frac{d}{dx}(-\cos(x^{2}))
limit as x approaches 2 of 6	\lim\:_{x\to\:2}(6)
limit as x approaches 0 of (sin(x)-x)/x	\lim\:_{x\to\:0}(\frac{\sin(x)-x}{x})
sum from n=1 to infinity of 4(3/4)^n	\sum\:_{n=1}^{\infty\:}4(\frac{3}{4})^{n}
integral of 2x*cos(1+3x^2)	\int\:2x\cdot\:\cos(1+3x^{2})dx
integral of ((7x^3-8sqrt(x)))/x	\int\:\frac{(7x^{3}-8\sqrt{x})}{x}dx
derivative of (5x^2+4/(x+3))	\frac{d}{dx}(\frac{5x^{2}+4}{x+3})
limit as x approaches-1 of ((1-x))/(x+1)	\lim\:_{x\to\:-1}(\frac{(1-x)}{x+1})
derivative of y=\sqrt[3]{6x^2+1}	derivative\:y=\sqrt[3]{6x^{2}+1}
derivative of-3^{-2}(tan(7t))^5	derivative\:-3^{-2}(\tan(7t))^{5}
limit as x approaches 3 of (x/3+2)/(x+1)	\lim\:_{x\to\:3}(\frac{\frac{x}{3}+2}{x+1})
derivative of (x^3/(x^2-4))	\frac{d}{dx}(\frac{x^{3}}{x^{2}-4})
derivative of (1+csc(x^6)/(1-cot(x^6)))	\frac{d}{dx}(\frac{1+\csc(x^{6})}{1-\cot(x^{6})})
area y=x^2-7x+6,x=2,x=6	area\:y=x^{2}-7x+6,x=2,x=6
derivative of ln(121sin^2(x))	derivative\:\ln(121\sin^{2}(x))
limit as x approaches-5 of (1/5+1/x)/(5+x)	\lim\:_{x\to\:-5}(\frac{\frac{1}{5}+\frac{1}{x}}{5+x})
limit as x approaches 1 of 1/((1-x))	\lim\:_{x\to\:1}(\frac{1}{(1-x)})
(d^2)/(dx^2)(6/(7t^5))	\frac{d^{2}}{dx^{2}}(\frac{6}{7t^{5}})
integral of 3e^{-0.4x}	\int\:3e^{-0.4x}dx
area x^2,(0,2)	area\:x^{2},(0,2)
integral of x^2sqrt(x^3+5)	\int\:x^{2}\sqrt{x^{3}+5}dx
inverse oflaplace 4/(s^2(s+2))+1/s	inverselaplace\:\frac{4}{s^{2}(s+2)}+\frac{1}{s}
derivative of 7log_{7}(x)	derivative\:7\log_{7}(x)
derivative of f(x)=e^{6x}	derivative\:f(x)=e^{6x}
limit as x approaches-2-of sqrt(x+2)	\lim\:_{x\to\:-2-}(\sqrt{x+2})
inverse oflaplace (7s+53)/(s^2+10s+61)	inverselaplace\:\frac{7s+53}{s^{2}+10s+61}
integral of cos(2x)cos(3x)	\int\:\cos(2x)\cos(3x)dx
limit as x approaches 3 of x/((x-3)^2)	\lim\:_{x\to\:3}(\frac{x}{(x-3)^{2}})
derivative of ln(x^2-6x+1)	\frac{d}{dx}(\ln(x^{2}-6x+1))
area y=4sqrt(x),y=4x	area\:y=4\sqrt{x},y=4x
integral from 0 to 0.5 of sin(t^2)	\int\:_{0}^{0.5}\sin(t^{2})dt
laplacetransform 3te^{-5t}	laplacetransform\:3te^{-5t}
integral of (5x+4y)	\int\:(5x+4y)dx
integral of sqrt((9+x)/(9-x))	\int\:\sqrt{\frac{9+x}{9-x}}dx
(\partial)/(\partial x)(xcos(y)+ye^x)	\frac{\partial\:}{\partial\:x}(x\cos(y)+ye^{x})
(3x+2sqrt(3x))^'	(3x+2\sqrt{3x})^{\prime\:}
tangent of f(x)=3x^3-3x,(-1,0)	tangent\:f(x)=3x^{3}-3x,(-1,0)
(\partial)/(\partial u)(4-u^2-v^2)	\frac{\partial\:}{\partial\:u}(4-u^{2}-v^{2})
integral of-2x-1	\int\:-2x-1dx
limit as x approaches infinity of 0*x	\lim\:_{x\to\:\infty\:}(0\cdot\:x)
integral of tan(x)sec^{3/2}(x)	\int\:\tan(x)\sec^{\frac{3}{2}}(x)dx
d/(dθ)(cos(4θ))	\frac{d}{dθ}(\cos(4θ))
sum from n=0 to infinity of (-1)^n(x^n)	\sum\:_{n=0}^{\infty\:}(-1)^{n}(x^{n})
(\partial)/(\partial t)(2sin(t))	\frac{\partial\:}{\partial\:t}(2\sin(t))
integral of 6sin^5(t)cos(t)	\int\:6\sin^{5}(t)\cos(t)dt
derivative of x(x^2-3)	\frac{d}{dx}(x(x^{2}-3))
d/(d{x)}(a(a-{x})(a-{y})(a-{z}))	\frac{d}{d{x}}(a(a-{x})(a-{y})(a-{z}))
integral of 6x-3	\int\:6x-3dx
area x^2+3x-2,-x^2-3x+6	area\:x^{2}+3x-2,-x^{2}-3x+6
sum from n=0 to infinity of (3/5)^{n/2}	\sum\:_{n=0}^{\infty\:}(\frac{3}{5})^{\frac{n}{2}}
derivative of ((3x-4/(5x+2))^{-5})	\frac{d}{dx}((\frac{3x-4}{5x+2})^{-5})
derivative of ln(x/(4x^2+x))	derivative\:\ln(\frac{x}{4x^{2}+x})
derivative of 1/2*\sqrt[3]{x}	\frac{d}{dx}(\frac{1}{2}\cdot\:\sqrt[3]{x})
integral from 0 to 1 of e^{-3x}	\int\:_{0}^{1}e^{-3x}dx
(\partial)/(\partial x)(1/y-2xsin(y))	\frac{\partial\:}{\partial\:x}(\frac{1}{y}-2x\sin(y))
derivative of ((e^x-1)/x)	\frac{d}{dx}(\frac{(e^{x}-1)}{x})
y^{''}-y^'-2y=-2t+6t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-2t+6t^{2}
derivative of e^{sin^2(x})	\frac{d}{dx}(e^{\sin^{2}(x)})
area y= 2/x ,y=8x,y= 1/2 x	area\:y=\frac{2}{x},y=8x,y=\frac{1}{2}x
derivative of 3/(4(2x-5^8))	\frac{d}{dx}(\frac{3}{4(2x-5)^{8}})
limit as x approaches-infinity of (sqrt(x^2+8x))/(8x+1)	\lim\:_{x\to\:-\infty\:}(\frac{\sqrt{x^{2}+8x}}{8x+1})
integral of ln(x)e^{-x}	\int\:\ln(x)e^{-x}dx
integral of (4x^2+3)/((x-5)^2)	\int\:\frac{4x^{2}+3}{(x-5)^{2}}dx
derivative of ((x+5(x^2-5x+25))/(x^3))	\frac{d}{dx}(\frac{(x+5)(x^{2}-5x+25)}{x^{3}})
integral of x^2sqrt(x^3+1)	\int\:x^{2}\sqrt{x^{3}+1}dx
derivative of sqrt(3x^2-x)	\frac{d}{dx}(\sqrt{3x^{2}-x})
derivative of f(x)=2000(x^2+5)^{1/3}	derivative\:f(x)=2000(x^{2}+5)^{\frac{1}{3}}
integral from 0 to 2 of e^{-x^2}	\int\:_{0}^{2}e^{-x^{2}}dx
(\partial)/(\partial x)(x^{0.5}+y)	\frac{\partial\:}{\partial\:x}(x^{0.5}+y)
derivative of 4x^3-10x^2	\frac{d}{dx}(4x^{3}-10x^{2})
(4x^2)^'	(4x^{2})^{\prime\:}

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