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Popular Calculus Problems

limit as x approaches 1-0 of 1/(1-x)	\lim\:_{x\to\:1-0}(\frac{1}{1-x})
limit as x approaches infinity+of xln(x)	\lim\:_{x\to\:\infty\:+}(x\ln(x))
derivative of f(x)=x^3-7x^2+6x+1	derivative\:f(x)=x^{3}-7x^{2}+6x+1
integral of x(4x+1)	\int\:x(4x+1)dx
derivative of sqrt((x^2-1/(x^2-2x+1)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-1}{x^{2}-2x+1}})
derivative of log_{4}(xe^x)	\frac{d}{dx}(\log_{4}(xe^{x}))
(dy)/(dx)+(2y)/(x+4)=(x+4)^7	\frac{dy}{dx}+\frac{2y}{x+4}=(x+4)^{7}
integral of 5sec^6(x)	\int\:5\sec^{6}(x)dx
integral from 3 to 8 of x/(x^2-1)	\int\:_{3}^{8}\frac{x}{x^{2}-1}dx
integral of cos(x-2y)	\int\:\cos(x-2y)dx
integral from 0 to infinity of xe^{-x/3}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{3}}dx
y^{''}+12y^'+35y=70t^2+48t+4+48e^t	y^{\prime\:\prime\:}+12y^{\prime\:}+35y=70t^{2}+48t+4+48e^{t}
laplacetransform h(t)=-5t^2	laplacetransform\:h(t)=-5t^{2}
derivative of (5sin(x)/(3+cos(x)))	\frac{d}{dx}(\frac{5\sin(x)}{3+\cos(x)})
integral from 1 to 4 of (2x+sqrt(x))	\int\:_{1}^{4}(2x+\sqrt{x})dx
integral of (2e^{3t})/(1+e^{6t)}	\int\:\frac{2e^{3t}}{1+e^{6t}}dt
limit as x approaches 2+of (\|x\|+2)/(x-2)	\lim\:_{x\to\:2+}(\frac{\left\|x\right\|+2}{x-2})
x(dy)/(dx)=y-x	x\frac{dy}{dx}=y-x
limit as x approaches 0 of ((cos(2x)-cos(3x)))/(x^2)	\lim\:_{x\to\:0}(\frac{(\cos(2x)-\cos(3x))}{x^{2}})
integral of (2x+3)sqrt(2x+1)	\int\:(2x+3)\sqrt{2x+1}dx
derivative of sech^2(3x)	\frac{d}{dx}(\sech^{2}(3x))
derivative of sqrt(1+36x)	\frac{d}{dx}(\sqrt{1+36x})
integral of (x+4)/(x^3+3x^2-10x)	\int\:\frac{x+4}{x^{3}+3x^{2}-10x}dx
tangent of f(x)=-2sin(x),\at x= 3/4 pi	tangent\:f(x)=-2\sin(x),\at\:x=\frac{3}{4}π
derivative of 1/(arccos(x^2+2x+4))	\frac{d}{dx}(\frac{1}{\arccos(x^{2}+2x+4)})
integral of 0e^x	\int\:0e^{x}dx
integral of 6e^{-5x}	\int\:6e^{-5x}dx
tangent of f(x)=1-x^2,\at x=2	tangent\:f(x)=1-x^{2},\at\:x=2
integral of (21)/(25+4r^2)	\int\:\frac{21}{25+4r^{2}}dr
integral of x^2*cos(nx)	\int\:x^{2}\cdot\:\cos(nx)dx
derivative of (2x/(x-4))	\frac{d}{dx}(\frac{2x}{x-4})
derivative of (2x/(sqrt(x^2+9)))	\frac{d}{dx}(\frac{2x}{\sqrt{x^{2}+9}})
inverse oflaplace (3s-15)/(2s^2-4s+10)	inverselaplace\:\frac{3s-15}{2s^{2}-4s+10}
tangent of f(x)= 2/(x+7),(-8,-2)	tangent\:f(x)=\frac{2}{x+7},(-8,-2)
sum from n=1 to infinity of (sin(8))^n	\sum\:_{n=1}^{\infty\:}(\sin(8))^{n}
limit as x approaches 0+of 4+ln(x)	\lim\:_{x\to\:0+}(4+\ln(x))
e^xy(dy)/(dx)=e^{-y}+e^{-5x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-5x-y}
integral of (x^2-3)sin(2x)	\int\:(x^{2}-3)\sin(2x)dx
derivative of e^{(-5x^2-2x^2})	\frac{d}{dx}(e^{(-5x^{2}-2x^{2})})
derivative of 11x	\frac{d}{dx}(11x)
integral of 5x-7	\int\:5x-7dx
y^'=ky*(100-y)	y^{\prime\:}=ky\cdot\:(100-y)
integral of (8+3x)/(1+x^2)	\int\:\frac{8+3x}{1+x^{2}}dx
integral of (sqrt(x^2-64))/(x^3)	\int\:\frac{\sqrt{x^{2}-64}}{x^{3}}dx
integral of ln(7x)	\int\:\ln(7x)dx
derivative of x^4+5cos(x)	\frac{d}{dx}(x^{4}+5\cos(x))
derivative of 5log_{10}(4x^2)	\frac{d}{dx}(5\log_{10}(4x^{2}))
integral of csc^3(4x)	\int\:\csc^{3}(4x)dx
derivative of (ln(x^3)/(ln(x^2)))	\frac{d}{dx}(\frac{\ln(x^{3})}{\ln(x^{2})})
integral of (3x+11)/(x^2-x-6)	\int\:\frac{3x+11}{x^{2}-x-6}dx
slope of y=-5x^{1/2}+x^{3/2}	slope\:y=-5x^{\frac{1}{2}}+x^{\frac{3}{2}}
derivative of (x^2+3x-1e^x)	\frac{d}{dx}((x^{2}+3x-1)e^{x})
limit as x approaches 9-of x^2-3x	\lim\:_{x\to\:9-}(x^{2}-3x)
integral of ((ln(x))^{7/2})/x	\int\:\frac{(\ln(x))^{\frac{7}{2}}}{x}dx
integral from-infinity to 2 of e^x	\int\:_{-\infty\:}^{2}e^{x}dx
limit as x approaches 2 of x^3+x^2+x	\lim\:_{x\to\:2}(x^{3}+x^{2}+x)
limit as x approaches 0 of (sin(7x))/(tan(11x))	\lim\:_{x\to\:0}(\frac{\sin(7x)}{\tan(11x)})
integral of cos(x)	\int\:\cos(x)dx
(\partial)/(\partial x)(cos(5x-2y^2))	\frac{\partial\:}{\partial\:x}(\cos(5x-2y^{2}))
tangent of x^2+8	tangent\:x^{2}+8
integral of (1/(x*ln(x)))	\int\:(\frac{1}{x\cdot\:\ln(x)})dx
derivative of f(x)=sqrt(4-x)	derivative\:f(x)=\sqrt{4-x}
integral of (x^2)/((x-1)^2)	\int\:\frac{x^{2}}{(x-1)^{2}}dx
integral of (x/(1+x^2))^2	\int\:(\frac{x}{1+x^{2}})^{2}dx
integral of 1/(x^2-25)	\int\:\frac{1}{x^{2}-25}dx
derivative of 1/(A^2sqrt(A))	derivative\:\frac{1}{A^{2}\sqrt{A}}
derivative of cot(2x^2-1)	\frac{d}{dx}(\cot(2x^{2}-1))
integral of (sqrt(x^2-64))/x	\int\:\frac{\sqrt{x^{2}-64}}{x}dx
derivative of (1+2x)/(3-4x)	derivative\:\frac{1+2x}{3-4x}
(\partial}{\partial x}(\frac{V(I,x))/I)	\frac{\partial\:}{\partial\:x}(\frac{V(I,x)}{I})
derivative of f(x)=7x^4	derivative\:f(x)=7x^{4}
integral of (x^5+x^3)^{11}(5x^4+3x^2)	\int\:(x^{5}+x^{3})^{11}(5x^{4}+3x^{2})dx
inverse oflaplace ((s-1))/(s^2(s^2+2))	inverselaplace\:\frac{(s-1)}{s^{2}(s^{2}+2)}
integral of sec^5(x/2)	\int\:\sec^{5}(\frac{x}{2})dx
derivative of ln(tan(7x))	\frac{d}{dx}(\ln(\tan(7x)))
derivative of f(x)=(x^7+5x)^{1/3}	derivative\:f(x)=(x^{7}+5x)^{\frac{1}{3}}
integral of x/(x-21)	\int\:\frac{x}{x-21}dx
integral from 0 to 1 of x^2+1	\int\:_{0}^{1}x^{2}+1dx
(d^2)/(dx^2)(xe^{-3x})	\frac{d^{2}}{dx^{2}}(xe^{-3x})
limit as x approaches 0 of 1/x*ln(x+1)	\lim\:_{x\to\:0}(\frac{1}{x}\cdot\:\ln(x+1))
integral of 6xyz+e^x	\int\:6xyz+e^{x}dy
limit as x approaches 0+of (x)ln(x^4)	\lim\:_{x\to\:0+}((x)\ln(x^{4}))
integral of 8cot^4(x)	\int\:8\cot^{4}(x)dx
derivative of x^{3/2}-1	\frac{d}{dx}(x^{\frac{3}{2}}-1)
derivative of 4asec(xtan(x))	\frac{d}{dx}(4a\sec(x)\tan(x))
(\partial)/(\partial x)(sin(ct)sin(x))	\frac{\partial\:}{\partial\:x}(\sin(ct)\sin(x))
(x+xy^2)dx+(e^{x^2}y)dy=0	(x+xy^{2})dx+(e^{x^{2}}y)dy=0
integral of (10x^2-19x+6)/(x^3-3x^2+2x)	\int\:\frac{10x^{2}-19x+6}{x^{3}-3x^{2}+2x}dx
laplacetransform sin(ω*t)	laplacetransform\:\sin(ω\cdot\:t)
integral of (sqrt(x^2-9))/(x^4)	\int\:\frac{\sqrt{x^{2}-9}}{x^{4}}dx
integral of x-1-ln(x)	\int\:x-1-\ln(x)dx
limit as x approaches infinity of-4	\lim\:_{x\to\:\infty\:}(-4)
inverse oflaplace e^{-pis}	inverselaplace\:e^{-πs}
derivative of sqrt(x^3+x^2+x+1)	derivative\:\sqrt{x^{3}+x^{2}+x+1}
derivative of (375/(x^4))	\frac{d}{dx}(\frac{375}{x^{4}})
integral of (tan^3(x))/(cos^2(x))	\int\:\frac{\tan^{3}(x)}{\cos^{2}(x)}dx
integral of-3e^{-x}	\int\:-3e^{-x}dx
integral of (x^2-4)^4(2x)	\int\:(x^{2}-4)^{4}(2x)dx
integral of (x^2)/((x^3-1)^4)	\int\:\frac{x^{2}}{(x^{3}-1)^{4}}dx
integral of 9sin^{-3/2}(x)cos^3(x)	\int\:9\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx

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