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Popular Calculus Problems

integral from a to infinity of 1/(x^2)	\int\:_{a}^{\infty\:}\frac{1}{x^{2}}dx
integral of x(18x+6)	\int\:x(18x+6)dx
integral from 0 to infinity of ye^{-3y}	\int\:_{0}^{\infty\:}ye^{-3y}dy
derivative of (x^2-1/(x^3+1))	\frac{d}{dx}(\frac{x^{2}-1}{x^{3}+1})
laplacetransform 12t^3-t^2	laplacetransform\:12t^{3}-t^{2}
derivative of 2x-4/(sqrt(x))	\frac{d}{dx}(2x-\frac{4}{\sqrt{x}})
integral of (x^2)/(sqrt(81+x^2))	\int\:\frac{x^{2}}{\sqrt{81+x^{2}}}dx
integral from 0 to 1 of sin(pi*x)	\int\:_{0}^{1}\sin(π\cdot\:x)dx
limit as x approaches 3 of (x^2-2)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-2}{x-3})
5x(x+6y)y^'=5y(x-6y)	5x(x+6y)y^{\prime\:}=5y(x-6y)
laplacetransform 10e^{2t}	laplacetransform\:10e^{2t}
tangent of-18x^2+9x+30	tangent\:-18x^{2}+9x+30
limit as x approaches 0-of x^{2/3}	\lim\:_{x\to\:0-}(x^{\frac{2}{3}})
y^'=e^{(-x/2)}	y^{\prime\:}=e^{(-\frac{x}{2})}
inverse oflaplace (p^3+1)^{-1}	inverselaplace\:(p^{3}+1)^{-1}
derivative of cos(ln(x^2))	\frac{d}{dx}(\cos(\ln(x^{2})))
derivative of 2cos(3x)	derivative\:2\cos(3x)
y^'+(2x)/(1+x^2)y=(e^{-x})/(1+x^2)	y^{\prime\:}+\frac{2x}{1+x^{2}}y=\frac{e^{-x}}{1+x^{2}}
limit as x approaches-1 of (-1^2+1)/(-1)	\lim\:_{x\to\:-1}(\frac{-1^{2}+1}{-1})
limit as x approaches infinity of x^{-1}	\lim\:_{x\to\:\infty\:}(x^{-1})
derivative of x^{4/5}	derivative\:x^{\frac{4}{5}}
(3xy^2+13y)+(3x^2y+13x)y^'=0	(3xy^{2}+13y)+(3x^{2}y+13x)y^{\prime\:}=0
integral of sqrt(x^2-1)	\int\:\sqrt{x^{2}-1}dx
derivative of u/(u^2+7)	derivative\:\frac{u}{u^{2}+7}
integral of t^{-1}	\int\:t^{-1}dt
integral of (4sqrt(x)-4/(sqrt(x)))	\int\:(4\sqrt{x}-\frac{4}{\sqrt{x}})dx
derivative of x^3(x-8)^2	derivative\:x^{3}(x-8)^{2}
tangent of y=(36)/(x^2+2),(1,12)	tangent\:y=\frac{36}{x^{2}+2},(1,12)
(\partial)/(\partial x)((ax-5)/(-y^2+1))	\frac{\partial\:}{\partial\:x}(\frac{ax-5}{-y^{2}+1})
limit as x approaches 0+of arctan(x)	\lim\:_{x\to\:0+}(\arctan(x))
integral of (x^4)/(sqrt(4+x^2))	\int\:\frac{x^{4}}{\sqrt{4+x^{2}}}dx
integral from-2 to 3 of x-4\|x\|	\int\:_{-2}^{3}x-4\left\|x\right\|dx
taylor 1/(x^2)	taylor\:\frac{1}{x^{2}}
derivative of 6^{3x-4}	\frac{d}{dx}(6^{3x-4})
integral from 0 to x of sin(pi/2 t^2)	\int\:_{0}^{x}\sin(\frac{π}{2}t^{2})dt
derivative of 2^x-x^2	\frac{d}{dx}(2^{x}-x^{2})
integral from 0 to 1 of x^2-x	\int\:_{0}^{1}x^{2}-xdx
derivative of y=(x+1)/(x-2)	derivative\:y=\frac{x+1}{x-2}
derivative of sqrt(9+x+y^2)	\frac{d}{dx}(\sqrt{9+x+y^{2}})
integral of x^{13}sin(x^{14})	\int\:x^{13}\sin(x^{14})dx
derivative of x^3-x^2-x	\frac{d}{dx}(x^{3}-x^{2}-x)
derivative of x^4-2x	\frac{d}{dx}(x^{4}-2x)
y^'=0.1ln((4000)/y)y	y^{\prime\:}=0.1\ln(\frac{4000}{y})y
integral of (e^{2x})/(sqrt(1+e^{2x))}	\int\:\frac{e^{2x}}{\sqrt{1+e^{2x}}}dx
integral from 0 to pi of 5sin^2(x)	\int\:_{0}^{π}5\sin^{2}(x)dx
integral of (ln(x^{3/2}))/x	\int\:\frac{\ln(x^{\frac{3}{2}})}{x}dx
integral from 0 to t of 3e^ssin(t-s)	\int\:_{0}^{t}3e^{s}\sin(t-s)ds
integral of 1/(2x+3)	\int\:\frac{1}{2x+3}dx
integral of (cos(x)sin(x))	\int\:(\cos(x)\sin(x))dx
limit as x approaches 0 of (2x)/(\|x\|)	\lim\:_{x\to\:0}(\frac{2x}{\left\|x\right\|})
(dy)/(dx)=(3xsqrt(y))	\frac{dy}{dx}=(3x\sqrt{y})
integral of 4x-x^3	\int\:4x-x^{3}dx
sum from i=1 to infinity of (1/2)^{i-1}	\sum\:_{i=1}^{\infty\:}(\frac{1}{2})^{i-1}
y^{''}-3y^'=2e^xsin(2x)	y^{\prime\:\prime\:}-3y^{\prime\:}=2e^{x}\sin(2x)
derivative of f(x)=(x-7)/(9x^2e^x)	derivative\:f(x)=\frac{x-7}{9x^{2}e^{x}}
(\partial)/(\partial x)((e^x-3)sin(y))	\frac{\partial\:}{\partial\:x}((e^{x}-3)\sin(y))
derivative of 3/(x^2)-8\sqrt[4]{x}	derivative\:\frac{3}{x^{2}}-8\sqrt[4]{x}
derivative of (3x+2(4x-3))	\frac{d}{dx}((3x+2)(4x-3))
derivative of (x^3-4x*e^{3x})	\frac{d}{dx}((x^{3}-4x)\cdot\:e^{3x})
y^{'''}-8=0	y^{\prime\:\prime\:\prime\:}-8=0
sum from n=0 to infinity of (2n)/(n^2)	\sum\:_{n=0}^{\infty\:}\frac{2n}{n^{2}}
(\partial)/(\partial y)((xy^2+x^3)^4)	\frac{\partial\:}{\partial\:y}((xy^{2}+x^{3})^{4})
derivative of 4ln(x+2cos(x)+x^4)	\frac{d}{dx}(4\ln(x)+2\cos(x)+x^{4})
tangent of f(x)=5x^2-5x,\at x=3	tangent\:f(x)=5x^{2}-5x,\at\:x=3
integral of (arctan(x/2))/(4+x^2)	\int\:\frac{\arctan(\frac{x}{2})}{4+x^{2}}dx
derivative of x^3-x+1	\frac{d}{dx}(x^{3}-x+1)
integral of (cosh(x))^3	\int\:(\cosh(x))^{3}dx
(\partial}{\partial x}(x^{1/2}+\frac{Y(x))/2)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}+\frac{Y(x)}{2})
derivative of f(x)=(x^2-1)/(x^2+x+1)	derivative\:f(x)=\frac{x^{2}-1}{x^{2}+x+1}
sum from k=2 to infinity of 2/(k^2-1)	\sum\:_{k=2}^{\infty\:}\frac{2}{k^{2}-1}
y^'+2y=e^{-t},y(0)= 3/2	y^{\prime\:}+2y=e^{-t},y(0)=\frac{3}{2}
laplacetransform 3	laplacetransform\:3
derivative of x^7sqrt(x^2-9x+9)	\frac{d}{dx}(x^{7}\sqrt{x^{2}-9x+9})
d/(dy)((2-x)(y-2)(3-x-y))	\frac{d}{dy}((2-x)(y-2)(3-x-y))
integral of (x+1)/(2x+1)	\int\:\frac{x+1}{2x+1}dx
integral of 5sin^2(x)	\int\:5\sin^{2}(x)dx
derivative of sqrt(2x^2-5x+4)	\frac{d}{dx}(\sqrt{2x^{2}-5x+4})
integral of (x-4)^2x^2	\int\:(x-4)^{2}x^{2}dx
(\partial)/(\partial x)(-3sin(2x))	\frac{\partial\:}{\partial\:x}(-3\sin(2x))
derivative of 2asin(x)	\frac{d}{dx}(2a\sin(x))
y^'+4y=e^{-x}	y^{\prime\:}+4y=e^{-x}
integral of (1+x^2)/(1+y^2)	\int\:\frac{1+x^{2}}{1+y^{2}}dx
(x^2+3y^2)dx-2xydy=0	(x^{2}+3y^{2})dx-2xydy=0
integral of (e^{2x})/(sqrt(1+e^x))	\int\:\frac{e^{2x}}{\sqrt{1+e^{x}}}dx
integral from 0 to 2pi of cos(x)sin(x)	\int\:_{0}^{2π}\cos(x)\sin(x)dx
limit as x approaches-6 of 11x+3	\lim\:_{x\to\:-6}(11x+3)
tangent of f(x)=12-x^2,(3,3)	tangent\:f(x)=12-x^{2},(3,3)
tangent of f(x)=(18)/(x^2+2),(1,6)	tangent\:f(x)=\frac{18}{x^{2}+2},(1,6)
limit as x approaches 0+of x^{11x}	\lim\:_{x\to\:0+}(x^{11x})
integral of e^{-6x}9x	\int\:e^{-6x}9xdx
derivative of 5x^5sin(2x)	\frac{d}{dx}(5x^{5}\sin(2x))
derivative of e^{(0.5x})	\frac{d}{dx}(e^{(0.5x)})
derivative of f(x)=\|x-5\|	derivative\:f(x)=\left\|x-5\right\|
x^{''}-2x-5=0	x^{\prime\:\prime\:}-2x-5=0
(\partial)/(\partial x)(e^{kx})	\frac{\partial\:}{\partial\:x}(e^{kx})
derivative of 10^{2sqrt(x)}	derivative\:10^{2\sqrt{x}}
integral of 6+6tan^2(x)	\int\:6+6\tan^{2}(x)dx
integral of-7	\int\:-7dx
integral from 0 to 1 of (x^2)/(x^3-5)	\int\:_{0}^{1}\frac{x^{2}}{x^{3}-5}dx
integral of (x^3)/(sqrt(x^2+121))	\int\:\frac{x^{3}}{\sqrt{x^{2}+121}}dx

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