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Popular Calculus Problems

integral of e^{-x}cos(x)	\int\:e^{-x}\cos(x)dx
derivative of ax^2+b	\frac{d}{dx}(ax^{2}+b)
derivative of 4xln(7x-4x)	\frac{d}{dx}(4x\ln(7x)-4x)
integral of-(sec^2(x)-1)/(tan(x))	\int\:-\frac{\sec^{2}(x)-1}{\tan(x)}dx
inverse oflaplace (s+3)/(s^2+s+1)	inverselaplace\:\frac{s+3}{s^{2}+s+1}
derivative of (1/(x^2-5/(x^4))(x+9x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{5}{x^{4}})(x+9x^{3}))
limit as x approaches 0+of ((3))/(x^2-x)	\lim\:_{x\to\:0+}(\frac{(3)}{x^{2}-x})
integral from 0 to 8 of x/((x+8)^3)	\int\:_{0}^{8}\frac{x}{(x+8)^{3}}dx
derivative of (3x^2-5xe^x)	\frac{d}{dx}((3x^{2}-5x)e^{x})
integral of x/(x-1)	\int\:\frac{x}{x-1}dx
derivative of y=(e^x)/(5x^2)	derivative\:y=\frac{e^{x}}{5x^{2}}
derivative of (2x+3^{1.4})	\frac{d}{dx}((2x+3)^{1.4})
(\partial)/(\partial x)(x+y^{1/2})	\frac{\partial\:}{\partial\:x}(x+y^{\frac{1}{2}})
limit as x approaches 0 of tan(7x)	\lim\:_{x\to\:0}(\tan(7x))
y^'=y^2e^{2x}	y^{\prime\:}=y^{2}e^{2x}
derivative of ln((2+x)/(1+x))	derivative\:\ln(\frac{2+x}{1+x})
(dy)/(dt)=sqrt(t)+t^2	\frac{dy}{dt}=\sqrt{t}+t^{2}
derivative of-x/(sqrt(1+x^2))	\frac{d}{dx}(-\frac{x}{\sqrt{1+x^{2}}})
integral of sqrt(13-x^2)	\int\:\sqrt{13-x^{2}}dx
(\partial)/(\partial z)(2ysin(x)+e^{2z})	\frac{\partial\:}{\partial\:z}(2y\sin(x)+e^{2z})
integral from 1/5 to 3 of 14xln(5x)	\int\:_{\frac{1}{5}}^{3}14x\ln(5x)dx
derivative of y=x^5ln(x)	derivative\:y=x^{5}\ln(x)
limit as x approaches 0 of (28^x-1)/x	\lim\:_{x\to\:0}(\frac{28^{x}-1}{x})
derivative of (arcsin(5x+5))^8	derivative\:(\arcsin(5x+5))^{8}
limit as x approaches-2 of (x+4)^3	\lim\:_{x\to\:-2}((x+4)^{3})
derivative of 30x^4-80x^3+60x^2-10	\frac{d}{dx}(30x^{4}-80x^{3}+60x^{2}-10)
derivative of 3x-4x^{7/8}	\frac{d}{dx}(3x-4x^{\frac{7}{8}})
limit as x approaches 0 of ((4e^x-4))/x	\lim\:_{x\to\:0}(\frac{(4e^{x}-4)}{x})
derivative of sin(2x^2*e^{-x})	\frac{d}{dx}(\sin(2x^{2}\cdot\:e^{-x}))
tangent of f(x)=(x-2)(2x+3),\at x=0	tangent\:f(x)=(x-2)(2x+3),\at\:x=0
integral of (x-5)*sin(x)	\int\:(x-5)\cdot\:\sin(x)dx
integral of (sin(x)tan(x))/(9+sec^2(x))	\int\:\frac{\sin(x)\tan(x)}{9+\sec^{2}(x)}dx
t^2y^{''}+21ty^'+100y=0	t^{2}y^{\prime\:\prime\:}+21ty^{\prime\:}+100y=0
limit as x approaches 2 of 5a+ax	\lim\:_{x\to\:2}(5a+ax)
(dy)/(dx)=(2-e^x)/(3+2y)	\frac{dy}{dx}=\frac{2-e^{x}}{3+2y}
derivative of (8x+7)^2	derivative\:(8x+7)^{2}
sum from n=1 to infinity of (ln(n))/(8n)	\sum\:_{n=1}^{\infty\:}\frac{\ln(n)}{8n}
integral of x^2sqrt(x^3+8)	\int\:x^{2}\sqrt{x^{3}+8}dx
derivative of x^3-12x^2+45x+9	\frac{d}{dx}(x^{3}-12x^{2}+45x+9)
limit as x approaches 2 of 7/(x-2)	\lim\:_{x\to\:2}(\frac{7}{x-2})
simplify 4/5 x^{5/4}	simplify\:\frac{4}{5}x^{\frac{5}{4}}
(\partial)/(\partial y)(-2y^4sin(2x))	\frac{\partial\:}{\partial\:y}(-2y^{4}\sin(2x))
integral from 1 to 2 of (x^2+2)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+2}{3x-x^{2}}dx
derivative of-2x^2-4x+1	derivative\:-2x^{2}-4x+1
((10)/x)^'	(\frac{10}{x})^{\prime\:}
limit as x approaches 8-of (x-8)/(x-8)	\lim\:_{x\to\:8-}(\frac{x-8}{x-8})
limit as x approaches 12 of (x-12)/(x^2-144)	\lim\:_{x\to\:12}(\frac{x-12}{x^{2}-144})
inverse oflaplace s/(s^2+8s+25)	inverselaplace\:\frac{s}{s^{2}+8s+25}
tangent of y=(2x+3)/(3x-2),(1,5)	tangent\:y=\frac{2x+3}{3x-2},(1,5)
tangent of f(x)=(x-3)/(6x-1),\at x=1	tangent\:f(x)=\frac{x-3}{6x-1},\at\:x=1
y^{''}+4y^'+4y=12te^{-2t}+4t	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=12te^{-2t}+4t
tangent of (x+2)^2+(y-3)^2=37,(-1,9)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-1,9)
integral of tan(4x)sec^2(4x)	\int\:\tan(4x)\sec^{2}(4x)dx
derivative of x^2-e^{y^2}	derivative\:x^{2}-e^{y^{2}}
derivative of y=arctan(e^x)	derivative\:y=\arctan(e^{x})
integral of 3x^2-6x	\int\:3x^{2}-6xdx
area f(x)=x^2+x-56,g(x)=-x^2+3x+4	area\:f(x)=x^{2}+x-56,g(x)=-x^{2}+3x+4
derivative of 1+a/r-b/(r^3)	derivative\:1+\frac{a}{r}-\frac{b}{r^{3}}
integral of (sec(x)tan(x))/(sec(x)-1)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)-1}dx
derivative of (x+2)(2x^2-3)	derivative\:(x+2)(2x^{2}-3)
integral of xe^{kx}	\int\:xe^{kx}dx
inverse oflaplace s+1-2.82j	inverselaplace\:s+1-2.82j
integral of 3x^2-18	\int\:3x^{2}-18dx
limit as x approaches 0 of x^2cos(20pix)	\lim\:_{x\to\:0}(x^{2}\cos(20πx))
integral of u/(1+u)	\int\:\frac{u}{1+u}du
integral of 1/(9-3x)	\int\:\frac{1}{9-3x}dx
y^{''}-2y^'+y=2(1-x)*cos(x)-2sin(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=2(1-x)\cdot\:\cos(x)-2\sin(x)
area 3x^2,x^4-x^2,[-2,2]	area\:3x^{2},x^{4}-x^{2},[-2,2]
integral of (30x^3-60x^2+7)/(x^2-2x)	\int\:\frac{30x^{3}-60x^{2}+7}{x^{2}-2x}dx
integral of (-15)/(x^2sqrt(x^2+4))	\int\:\frac{-15}{x^{2}\sqrt{x^{2}+4}}dx
integral of 3(x^4)/(e^{x^5)}	\int\:3\frac{x^{4}}{e^{x^{5}}}dx
integral from 0 to pi/4 of 1	\int\:_{0}^{\frac{π}{4}}1
derivative of 9x+1-x^2	derivative\:9x+1-x^{2}
limit as x approaches 1 of (x^2-3x)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}-3x}{x-1})
integral of (e^{2y})/(sqrt(e^y-1))	\int\:\frac{e^{2y}}{\sqrt{e^{y}-1}}dy
integral of tcos^5(t^2)	\int\:t\cos^{5}(t^{2})dt
derivative of y=sqrt(1+2e^{8x)}	derivative\:y=\sqrt{1+2e^{8x}}
sum from n=1 to infinity of 1/(7n^2+n+6)	\sum\:_{n=1}^{\infty\:}\frac{1}{7n^{2}+n+6}
derivative of-ce^{-x}	\frac{d}{dx}(-ce^{-x})
integral of 1/((2x-3)(3x^2+x))	\int\:\frac{1}{(2x-3)(3x^{2}+x)}dx
integral from 0 to 1 of xe^x-e^x	\int\:_{0}^{1}xe^{x}-e^{x}dx
y^{''}+4y=sec(2t)	y^{\prime\:\prime\:}+4y=\sec(2t)
(\partial)/(\partial x)((2x+1)^y)	\frac{\partial\:}{\partial\:x}((2x+1)^{y})
integral of 10csc^2(5x)cot(5x)	\int\:10\csc^{2}(5x)\cot(5x)dx
(\partial)/(\partial x)((sin(x+y))/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{\sin(x+y)}{y^{2}})
4(dy)/(dx)-12x^2=0	4\frac{dy}{dx}-12x^{2}=0
derivative of y=(80)/(x^6)	derivative\:y=\frac{80}{x^{6}}
derivative of y=sqrt(3x)+2cos(x)	derivative\:y=\sqrt{3x}+2\cos(x)
integral of 6e^{4x}	\int\:6e^{4x}dx
(\partial)/(\partial x)((x-y)^n)	\frac{\partial\:}{\partial\:x}((x-y)^{n})
integral from 0 to 1 of x^2arctan(x)	\int\:_{0}^{1}x^{2}\arctan(x)dx
sum from n=1 to infinity of (10)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{10}{3^{n}}
integral from 0 to 1 of 1/((x+1)(x-2))	\int\:_{0}^{1}\frac{1}{(x+1)(x-2)}dx
integral of (sqrt(x^2-a^2))/x	\int\:\frac{\sqrt{x^{2}-a^{2}}}{x}dx
(\partial)/(\partial y)(cos(x^2)sin(yz))	\frac{\partial\:}{\partial\:y}(\cos(x^{2})\sin(yz))
(dy)/(dx)=(y^2+4xsqrt(x^2+y^2))/(xy)	\frac{dy}{dx}=\frac{y^{2}+4x\sqrt{x^{2}+y^{2}}}{xy}
f(x)= 1/(x^5)	f(x)=\frac{1}{x^{5}}
derivative of f(x)=(x^3-3x)(2x^2+3x+5)	derivative\:f(x)=(x^{3}-3x)(2x^{2}+3x+5)
integral of 2sin(θ)-sec^2(θ)	\int\:2\sin(θ)-\sec^{2}(θ)dθ
limit as x approaches+0 of x/(arctan(x))	\lim\:_{x\to\:+0}(\frac{x}{\arctan(x)})

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