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Popular Calculus Problems

inverse oflaplace 7/(s^3+2s^2+9s+18)	inverselaplace\:\frac{7}{s^{3}+2s^{2}+9s+18}
integral of (3/(x^{1/3)}-3x^{2/3})	\int\:(\frac{3}{x^{\frac{1}{3}}}-3x^{\frac{2}{3}})dx
derivative of (36x)/(x^2+36)	derivative\:\frac{36x}{x^{2}+36}
derivative of-4e^{12x}	\frac{d}{dx}(-4e^{12x})
integral of (3^4+x^{15})	\int\:(3^{4}+x^{15})dx
integral of x^2sqrt(a^2-x^2)	\int\:x^{2}\sqrt{a^{2}-x^{2}}dx
f(x)=sqrt(x^3-x)	f(x)=\sqrt{x^{3}-x}
y^{''}+4y^'+4y=64cos(2x)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=64\cos(2x)
integral of (y-2)	\int\:(y-2)dy
derivative of (cos(3x)/x)	\frac{d}{dx}(\frac{\cos(3x)}{x})
tangent of y=(2x-1)(x+4),(1,5)	tangent\:y=(2x-1)(x+4),(1,5)
derivative of (12)/(x^5)-7/(\sqrt[5]{x)}	derivative\:\frac{12}{x^{5}}-\frac{7}{\sqrt[5]{x}}
derivative of sqrt((x^3-2x^{x^2-3)})	\frac{d}{dx}(\sqrt{(x^{3}-2x)^{x^{2}-3}})
derivative of x^2e^xsin(x)	\frac{d}{dx}(x^{2}e^{x}\sin(x))
derivative of f(x)=(x+9)/(x^2-7x+1)	derivative\:f(x)=\frac{x+9}{x^{2}-7x+1}
integral of x*sin(x^2)	\int\:x\cdot\:\sin(x^{2})dx
integral from-2 to 2 of x^2sqrt(1+4x^2)	\int\:_{-2}^{2}x^{2}\sqrt{1+4x^{2}}dx
integral of 5sin(6pix)	\int\:5\sin(6πx)dx
simplify ln((5x+2)(3x-4)^2)	simplify\:\ln((5x+2)(3x-4)^{2})
y^{''}-4y^'+4y=x^2	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=x^{2}
taylor (x+1)^{1/2}	taylor\:(x+1)^{\frac{1}{2}}
y^'=6x(y-1)^{2/3}	y^{\prime\:}=6x(y-1)^{\frac{2}{3}}
sum from k=0 to infinity of k/(2^k)x^k	\sum\:_{k=0}^{\infty\:}\frac{k}{2^{k}}x^{k}
y^{''}+2sqrt(14)y^'+14y=0	y^{\prime\:\prime\:}+2\sqrt{14}y^{\prime\:}+14y=0
y^'+3/x y=x^2y^2	y^{\prime\:}+\frac{3}{x}y=x^{2}y^{2}
(\partial)/(\partial x)(e^{3x}cos(2x))	\frac{\partial\:}{\partial\:x}(e^{3x}\cos(2x))
integral of 1/(x^4)	\int\:\frac{1}{x^{4}}dx
derivative of (x^2/(1+x))	\frac{d}{dx}(\frac{x^{2}}{1+x})
derivative of 5/(x+1)	derivative\:\frac{5}{x+1}
derivative of sec(sqrt(x))	\frac{d}{dx}(\sec(\sqrt{x}))
integral from 1 to 2 of 11e^{1/x}	\int\:_{1}^{2}11e^{\frac{1}{x}}dx
derivative of log_{4}(e^{-x}cos(pix))	derivative\:\log_{4}(e^{-x}\cos(πx))
integral of 4cos(θ)sin(θ)	\int\:4\cos(θ)\sin(θ)dθ
limit as x approaches 0+of (e^x-1)/x	\lim\:_{x\to\:0+}(\frac{e^{x}-1}{x})
inverse oflaplace 1/((s+1)^{1/2)}	inverselaplace\:\frac{1}{(s+1)^{\frac{1}{2}}}
slope of (-6,4),(-1,4)	slope\:(-6,4),(-1,4)
derivative of (x^{n-1}/n)	\frac{d}{dx}(\frac{x^{n-1}}{n})
integral from x to 2x of y	\int\:_{x}^{2x}ydy
sum from n=0 to infinity of (n^3)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{3}}{5^{n}}
(\partial)/(\partial x)(2x^3y+sin(x^2))	\frac{\partial\:}{\partial\:x}(2x^{3}y+\sin(x^{2}))
tangent of f(x)=(4x)/(x^2-5),(3,3)	tangent\:f(x)=\frac{4x}{x^{2}-5},(3,3)
limit as x approaches 7 of (x+2)/(x-7)	\lim\:_{x\to\:7}(\frac{x+2}{x-7})
integral of (e^{3x}+1)/(e^{2x)}	\int\:\frac{e^{3x}+1}{e^{2x}}dx
integral from 0 to 1 of (x-6)/(x^2-5x+6)	\int\:_{0}^{1}\frac{x-6}{x^{2}-5x+6}dx
(dy)/(dx)-e^{8x+y}=0	\frac{dy}{dx}-e^{8x+y}=0
integral of x*sin(2ax)	\int\:x\cdot\:\sin(2ax)dx
derivative of sqrt(cos(e^{x^{2cos(x))})}	derivative\:\sqrt{\cos(e^{x^{2\cos(x)}})}
derivative of 5e^{-x}-3e^{-5x}	\frac{d}{dx}(5e^{-x}-3e^{-5x})
derivative of f(x)=(x^2+1)*e^{x-1}	derivative\:f(x)=(x^{2}+1)\cdot\:e^{x-1}
81y^{''}+72y^'+16y=0,y^'(0)=-1	81y^{\prime\:\prime\:}+72y^{\prime\:}+16y=0,y^{\prime\:}(0)=-1
derivative of x^{9/4}+e^{-2x}	\frac{d}{dx}(x^{\frac{9}{4}}+e^{-2x})
2(dy)/(dx)+6y+4=0	2\frac{dy}{dx}+6y+4=0
derivative of f(x)=(3x^2+3x-1)^4	derivative\:f(x)=(3x^{2}+3x-1)^{4}
integral of xsin(x)cos(x)	\int\:x\cdot\:\sin(x)\cdot\:\cos(x)dx
derivative of y=ln(4/x)	derivative\:y=\ln(\frac{4}{x})
derivative of f(x)=(2x-6)^4(x^2+x+1)^5	derivative\:f(x)=(2x-6)^{4}(x^{2}+x+1)^{5}
area y=xe-0.1x,y=0,x=3	area\:y=xe-0.1x,y=0,x=3
(\partial)/(\partial y)(x/y+e^y)	\frac{\partial\:}{\partial\:y}(\frac{x}{y}+e^{y})
tangent of f(x)=-3cos(x),\at x=(3pi)/4	tangent\:f(x)=-3\cos(x),\at\:x=\frac{3π}{4}
derivative of sin(wx)	\frac{d}{dx}(\sin(wx))
integral of 15sec^4(x)	\int\:15\sec^{4}(x)dx
tangent of f(x)=x^2-9,(-5,16)	tangent\:f(x)=x^{2}-9,(-5,16)
derivative of tan(x)-1	derivative\:\tan(x)-1
integral of e^{xy}+xye^{xy}	\int\:e^{xy}+xye^{xy}dy
3y+x^4(dy)/(dx)=2xy	3y+x^{4}\frac{dy}{dx}=2xy
integral of (7x)/(sqrt(1-x^2))	\int\:\frac{7x}{\sqrt{1-x^{2}}}dx
derivative of y=cot(2)(cos(x))	derivative\:y=\cot(2)(\cos(x))
derivative of 5^{x-1}	\frac{d}{dx}(5^{x-1})
derivative of G(t)=(4t)/(t+1)	derivative\:G(t)=\frac{4t}{t+1}
tangent of f(x)=x^2+5x,\at x=4	tangent\:f(x)=x^{2}+5x,\at\:x=4
integral of xe^{-x}-e^{-x}	\int\:xe^{-x}-e^{-x}dx
(\partial)/(\partial x)(3e^{3x})	\frac{\partial\:}{\partial\:x}(3e^{3x})
y^'=y(1-y),y(0)=8	y^{\prime\:}=y(1-y),y(0)=8
derivative of xcos(x)-sin(x)	derivative\:x\cos(x)-\sin(x)
derivative of 1/6 pir^3	derivative\:\frac{1}{6}πr^{3}
derivative of ln(sinh(9x))	\frac{d}{dx}(\ln(\sinh(9x)))
(dy)/(dx)=(y^2-1)/(x^2-1),y(8)=8	\frac{dy}{dx}=\frac{y^{2}-1}{x^{2}-1},y(8)=8
derivative of (x^2+x^3)	\frac{d}{dx}((x^{2}+x)^{3})
derivative of (1+x^2/(1-x^2))	\frac{d}{dx}(\frac{1+x^{2}}{1-x^{2}})
integral from 1 to 2 of (11)/(x^3+3x)	\int\:_{1}^{2}\frac{11}{x^{3}+3x}dx
integral of 1/(x^2*sqrt(9+x^2))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{9+x^{2}}}dx
integral of x(cos(x))^2	\int\:x(\cos(x))^{2}dx
integral of x/(sqrt(25+x^2))	\int\:\frac{x}{\sqrt{25+x^{2}}}dx
derivative of G(r)=sqrt(r)+\sqrt[9]{r}	derivative\:G(r)=\sqrt{r}+\sqrt[9]{r}
tangent of f(x)=2x^3+3x^2-12x+5	tangent\:f(x)=2x^{3}+3x^{2}-12x+5
limit as n approaches infinity of n-1	\lim\:_{n\to\:\infty\:}(n-1)
(dy)/(dx)=(x^2)/(y(1+x^3))	\frac{dy}{dx}=\frac{x^{2}}{y(1+x^{3})}
derivative of y=(4x+1)/(sqrt(x))	derivative\:y=\frac{4x+1}{\sqrt{x}}
derivative of-(5e^{5/x})/(x^2)	derivative\:-\frac{5e^{\frac{5}{x}}}{x^{2}}
laplacetransform 200e^{-2t}+100e^{-t}+10	laplacetransform\:200e^{-2t}+100e^{-t}+10
(dy)/(dx)+2xy=x	\frac{dy}{dx}+2xy=x
limit as x approaches 1 of sqrt(x-2)	\lim\:_{x\to\:1}(\sqrt{x-2})
d/(dy)(e^xcos(xy))	\frac{d}{dy}(e^{x}\cos(xy))
slope ofintercept (-3,-8),(4,6)	slopeintercept\:(-3,-8),(4,6)
integral of 1/(sqrt(x^2-2))	\int\:\frac{1}{\sqrt{x^{2}-2}}dx
integral of (sqrt(x)+1/(4sqrt(x)))	\int\:(\sqrt{x}+\frac{1}{4\sqrt{x}})dx
laplacetransform h(t)=t-2	laplacetransform\:h(t)=t-2
integral of x(x+6)^7	\int\:x(x+6)^{7}dx
(\partial)/(\partial y)(cos(x)+xcos(y)-y)	\frac{\partial\:}{\partial\:y}(\cos(x)+x\cos(y)-y)
sum from n=0 to infinity of (2/4)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{4})^{n}

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