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Popular Calculus Problems

limit as x approaches infinity of x^6e^{-x^5}	\lim\:_{x\to\:\infty\:}(x^{6}e^{-x^{5}})
integral of sinh(1+4x)	\int\:\sinh(1+4x)dx
laplacetransform (t^2+1/2)^2	laplacetransform\:(t^{2}+\frac{1}{2})^{2}
(x^2+2y^2)dx-xydy=0	(x^{2}+2y^{2})dx-xydy=0
tangent of y=2sin(x),\at x= 3/4 pi	tangent\:y=2\sin(x),\at\:x=\frac{3}{4}π
derivative of h(x)=(3x^3-3)/(ln(x))	derivative\:h(x)=\frac{3x^{3}-3}{\ln(x)}
area y= 3/x ,y=9x,y= 1/(9x)	area\:y=\frac{3}{x},y=9x,y=\frac{1}{9x}
integral from-pi/2 to pi/2 of cos(x)	\int\:_{-\frac{π}{2}}^{\frac{π}{2}}\cos(x)dx
integral of (22)/(22+e^x)	\int\:\frac{22}{22+e^{x}}dx
integral of (2x+1)/(x^2-2x+5)	\int\:\frac{2x+1}{x^{2}-2x+5}dx
integral of csc^4(θ)	\int\:\csc^{4}(θ)dθ
derivative of 6te^{-t}	derivative\:6te^{-t}
integral of x^2e^{13x}	\int\:x^{2}e^{13x}dx
limit as x approaches 8 of 1/((x-8))	\lim\:_{x\to\:8}(\frac{1}{(x-8)})
integral of pi(2sqrt(y))^2	\int\:π(2\sqrt{y})^{2}dy
integral of 2xln(x-2)	\int\:2x\ln(x-2)dx
integral from 1 to 6 of 3/(x^2+2x+1)	\int\:_{1}^{6}\frac{3}{x^{2}+2x+1}dx
limit as x approaches infinity of (4x+2)/(2x-7)	\lim\:_{x\to\:\infty\:}(\frac{4x+2}{2x-7})
y^{''}-6y^'+18y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+18y=0
integral of (3x+4)^{5/2}	\int\:(3x+4)^{\frac{5}{2}}dx
derivative of sqrt(1+x)	derivative\:\sqrt{1+x}
limit as x approaches 0+of x^2e^{1/x}	\lim\:_{x\to\:0+}(x^{2}e^{\frac{1}{x}})
derivative of 2e^{-2x}+1/3 e^x	\frac{d}{dx}(2e^{-2x}+\frac{1}{3}e^{x})
derivative of 6^{x^2-3}	\frac{d}{dx}(6^{x^{2}-3})
derivative of (x-sqrt(x)/(x^2))	\frac{d}{dx}(\frac{x-\sqrt{x}}{x^{2}})
integral of (x^2)/(x^2-6x+9)	\int\:\frac{x^{2}}{x^{2}-6x+9}dx
derivative of (2x^2-7)/(8x^3+1)	derivative\:\frac{2x^{2}-7}{8x^{3}+1}
derivative of (sqrt(x^2+y^2-9)/x)	\frac{d}{dx}(\frac{\sqrt{x^{2}+y^{2}-9}}{x})
sum from n=1 to infinity}(-1^{n+1 of)/n	\sum\:_{n=1}^{\infty\:}\frac{-1^{n+1}}{n}
integral of x^2cos(1/2 x)	\int\:x^{2}\cos(\frac{1}{2}x)dx
integral from 0 to 1 of 6/(1+t^2)	\int\:_{0}^{1}\frac{6}{1+t^{2}}dt
derivative of (cos(x)/x+x/(cos(x)))	\frac{d}{dx}(\frac{\cos(x)}{x}+\frac{x}{\cos(x)})
derivative of 1/(sqrt(4x^2+1))	derivative\:\frac{1}{\sqrt{4x^{2}+1}}
limit as x approaches 0+of (x^2)/9-2/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{9}-\frac{2}{x})
integral of 1/(x^{1/2)+x^{3/2}}	\int\:\frac{1}{x^{\frac{1}{2}}+x^{\frac{3}{2}}}dx
tangent of f(x)=-5-2x^2,(-3,-23)	tangent\:f(x)=-5-2x^{2},(-3,-23)
y^'+e^xy=2e^x	y^{\prime\:}+e^{x}y=2e^{x}
integral of e^{2x}cos(4x)	\int\:e^{2x}\cos(4x)dx
derivative of (ln(x)^{-2})	\frac{d}{dx}((\ln(x))^{-2})
sum from n=0 to infinity of 1/((2n)!)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n)!}
area y=\sqrt[3]{2x},y= 1/8 x^2	area\:y=\sqrt[3]{2x},y=\frac{1}{8}x^{2}
derivative of arctan(sqrt(x^2+2x)+C)	\frac{d}{dx}(\arctan(\sqrt{x^{2}+2x})+C)
integral of x/(sqrt(1+5x^2))	\int\:\frac{x}{\sqrt{1+5x^{2}}}dx
derivative of y=3x^2+1/x	derivative\:y=3x^{2}+\frac{1}{x}
integral of 7cos^3(3x)	\int\:7\cos^{3}(3x)dx
derivative of f(x)=cos(2sin(x))	derivative\:f(x)=\cos(2\sin(x))
derivative of ln(x+sqrt(4+x^2))	\frac{d}{dx}(\ln(x+\sqrt{4+x^{2}}))
laplacetransform 5cos(2t)	laplacetransform\:5\cos(2t)
derivative of sin^3(2x+x^2)	\frac{d}{dx}(\sin^{3}(2x)+x^{2})
y^{''}-4y+3y=0	y^{\prime\:\prime\:}-4y+3y=0
integral from-2 to 3 of 2xsqrt(2x^2-3)	\int\:_{-2}^{3}2x\sqrt{2x^{2}-3}dx
integral of (sqrt(5x)+sqrt(5/x))	\int\:(\sqrt{5x}+\sqrt{\frac{5}{x}})dx
derivative of (5x/(1+x^2))	\frac{d}{dx}(\frac{5x}{1+x^{2}})
limit as x approaches 1 of x/(4x-1)	\lim\:_{x\to\:1}(\frac{x}{4x-1})
derivative of (8x^2-16x+16)e^x	derivative\:(8x^{2}-16x+16)e^{x}
(d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x)	\frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=10\sin(x)
integral of 2sin(sqrt(x))	\int\:2\sin(\sqrt{x})dx
limit as x approaches 1 of-2x^2+5x+4	\lim\:_{x\to\:1}(-2x^{2}+5x+4)
integral of (csc^2(2x))/(4-cot(2x))	\int\:\frac{\csc^{2}(2x)}{4-\cot(2x)}dx
integral of sin^2(x)cos(nx)	\int\:\sin^{2}(x)\cos(nx)dx
derivative of (cos(sqrt(x))/(2sqrt(x)))	\frac{d}{dx}(\frac{\cos(\sqrt{x})}{2\sqrt{x}})
tangent of f(x)=9-3x+2x^2,\at x=-6	tangent\:f(x)=9-3x+2x^{2},\at\:x=-6
derivative of 2x-3x^{2/3}	\frac{d}{dx}(2x-3x^{\frac{2}{3}})
integral of 25e^{-2x}	\int\:25e^{-2x}dx
limit as x approaches pi/2-of cot(2x)	\lim\:_{x\to\:\frac{π}{2}-}(\cot(2x))
derivative of xsqrt(9-x^2)	\frac{d}{dx}(x\sqrt{9-x^{2}})
integral from 3 to 7 of e^x	\int\:_{3}^{7}e^{x}dx
(\partial)/(\partial x)(ln(4x^2+3y^2+6))	\frac{\partial\:}{\partial\:x}(\ln(4x^{2}+3y^{2}+6))
integral of (3+x)/(3-x)	\int\:\frac{3+x}{3-x}dx
integral of e^{5x}sin(4x)	\int\:e^{5x}\sin(4x)dx
derivative of (5x^2-3(x^2+x+4))	\frac{d}{dx}((5x^{2}-3)(x^{2}+x+4))
derivative of 1/((3x^3+5x+7^{3/4)})	\frac{d}{dx}(\frac{1}{(3x^{3}+5x+7)^{\frac{3}{4}}})
limit as x approaches 16 of 4-sqrt(x)	\lim\:_{x\to\:16}(4-\sqrt{x})
derivative of f(x)=(2x^5-3)^8	derivative\:f(x)=(2x^{5}-3)^{8}
limit as x approaches+(-2.4) of x	\lim\:_{x\to\:+(-2.4)}(x)
sum from n=7 to infinity of 1/n	\sum\:_{n=7}^{\infty\:}\frac{1}{n}
limit as x approaches-5 of (x-1)/(x+5)	\lim\:_{x\to\:-5}(\frac{x-1}{x+5})
integral of 5/(16+9cos^2(x))	\int\:\frac{5}{16+9\cos^{2}(x)}dx
(\partial)/(\partial x)(ln((y/x)^2))	\frac{\partial\:}{\partial\:x}(\ln((\frac{y}{x})^{2}))
integral of (x^2-8x-17)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-8x-17}{(x-1)^{2}(x^{2}+1)}dx
(\partial)/(\partial x)(sin(2y))	\frac{\partial\:}{\partial\:x}(\sin(2y))
limit as x approaches 1 of \|x\|	\lim\:_{x\to\:1}(\left\|x\right\|)
integral from 0 to 7 of te^{-t}	\int\:_{0}^{7}te^{-t}dt
integral from 0 to infinity of (e^{-x/a})/a	\int\:_{0}^{\infty\:}\frac{e^{-\frac{x}{a}}}{a}dx
integral of (4x+3)^4	\int\:(4x+3)^{4}dx
d/(dt)((\sqrt[3]{t})/(t-3))	\frac{d}{dt}(\frac{\sqrt[3]{t}}{t-3})
integral of-2xsin(x)	\int\:-2x\sin(x)dx
derivative of log_{2}(log_{2}(x))	derivative\:\log_{2}(\log_{2}(x))
integral of x/(sqrt(3x^2+1))	\int\:\frac{x}{\sqrt{3x^{2}+1}}dx
derivative of (t+4)^{2/3}(2t^2-3)^3	derivative\:(t+4)^{\frac{2}{3}}(2t^{2}-3)^{3}
tangent of f(x)=\|x-4\|,\at x=0	tangent\:f(x)=\left\|x-4\right\|,\at\:x=0
derivative of 0x	\frac{d}{dx}(0x)
integral from 0 to pi/4 of 3sec^2(x)	\int\:_{0}^{\frac{π}{4}}3\sec^{2}(x)dx
integral of ((x^2-5x)^2)/(sqrt(x))	\int\:\frac{(x^{2}-5x)^{2}}{\sqrt{x}}dx
integral of (x^2+4)/(3x^3+4x^2-4x)	\int\:\frac{x^{2}+4}{3x^{3}+4x^{2}-4x}dx
tangent of f(x)=sqrt(2x+45),\at x=2	tangent\:f(x)=\sqrt{2x+45},\at\:x=2
derivative of 49+23sin((2pi)/(52)(t-10))	derivative\:49+23\sin(\frac{2π}{52}(t-10))
integral of 1/(xsqrt(1-ln(x^2)))	\int\:\frac{1}{x\sqrt{1-\ln(x^{2})}}dx
y^'=(2x)/y	y^{\prime\:}=\frac{2x}{y}
integral of 4x-6	\int\:4x-6dx

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