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Popular Calculus Problems

integral of (x^2-5)^52x	\int\:(x^{2}-5)^{5}2xdx
integral of 7arctan(sqrt(x))	\int\:7\arctan(\sqrt{x})dx
limit as x approaches 0+of 5sin(x)ln(x)	\lim\:_{x\to\:0+}(5\sin(x)\ln(x))
(\partial)/(\partial x)(7e^{x^7y})	\frac{\partial\:}{\partial\:x}(7e^{x^{7}y})
derivative of 1/(2sqrt(x)+1/(6x^{5/6)})	\frac{d}{dx}(\frac{1}{2\sqrt{x}}+\frac{1}{6x^{\frac{5}{6}}})
(\partial)/(\partial x)((y+xy)/((1+x)^3))	\frac{\partial\:}{\partial\:x}(\frac{y+xy}{(1+x)^{3}})
derivative of e^{5x}*5	\frac{d}{dx}(e^{5x}\cdot\:5)
derivative of sqrt(u+1)(1-8u^2)^7	derivative\:\sqrt{u+1}(1-8u^{2})^{7}
derivative of e^{-bt}	derivative\:e^{-bt}
limit as x approaches-2-of (1-x)/(x^3+8)	\lim\:_{x\to\:-2-}(\frac{1-x}{x^{3}+8})
derivative of (1+i^x)	\frac{d}{dx}((1+i)^{x})
(\partial)/(\partial x)((4x+8)ln(6xy))	\frac{\partial\:}{\partial\:x}((4x+8)\ln(6xy))
derivative of 4e^{-3x}	\frac{d}{dx}(4e^{-3x})
derivative of-cos(2x-2sin(2x)(1-x))	\frac{d}{dx}(-\cos(2x)-2\sin(2x)(1-x))
x(dy)/(dx)+2y=x^2	x\frac{dy}{dx}+2y=x^{2}
limit as x approaches 0 of x/(sin^2(x))	\lim\:_{x\to\:0}(\frac{x}{\sin^{2}(x)})
derivative of x/(8x+3)	\frac{d}{dx}(\frac{x}{8x+3})
(dy)/(dx)=(3-2y)*x^3	\frac{dy}{dx}=(3-2y)\cdot\:x^{3}
integral of (ln(x))/(x(1+ln^2(x)))	\int\:\frac{\ln(x)}{x(1+\ln^{2}(x))}dx
derivative of (5x^2-2(x^3+3x))	\frac{d}{dx}((5x^{2}-2)(x^{3}+3x))
derivative of 3x\sqrt[4]{x^4-2}	\frac{d}{dx}(3x\sqrt[4]{x^{4}-2})
derivative of 4x^3+2+1/x	\frac{d}{dx}(4x^{3}+2+\frac{1}{x})
(\partial)/(\partial x)(xsin(2x))	\frac{\partial\:}{\partial\:x}(x\sin(2x))
(\partial)/(\partial x)(xe^{x/y})	\frac{\partial\:}{\partial\:x}(xe^{\frac{x}{y}})
slope of (6,-12),(10,-8)	slope\:(6,-12),(10,-8)
integral of (((ln(x))^3))/x	\int\:\frac{((\ln(x))^{3})}{x}dx
derivative of f(x)=2x^{1/2}	derivative\:f(x)=2x^{\frac{1}{2}}
integral of 3sin^2(x)cos^4(x)	\int\:3\sin^{2}(x)\cos^{4}(x)dx
integral from 0 to 3 of (x-1)(x-2)(x-3)	\int\:_{0}^{3}(x-1)(x-2)(x-3)dx
slope ofintercept (-7,-9),(0,-7)	slopeintercept\:(-7,-9),(0,-7)
integral of (4-y^2)^{1/2}	\int\:(4-y^{2})^{\frac{1}{2}}dy
derivative of sin(1-xcos^3(x))	\frac{d}{dx}(\sin(1-x)\cos^{3}(x))
derivative of f(x)=(e^x)/(2+5x)	derivative\:f(x)=\frac{e^{x}}{2+5x}
sqrt(x)+(sqrt(y)dy)/(dx)=0	\sqrt{x}+\frac{\sqrt{y}dy}{dx}=0
6y^'-2y=xy^4,y(0)=-2	6y^{\prime\:}-2y=xy^{4},y(0)=-2
derivative of f(x)=(6x+16)/(x+3)	derivative\:f(x)=\frac{6x+16}{x+3}
derivative of xsqrt(x)+x^2sqrt(x)	\frac{d}{dx}(x\sqrt{x}+x^{2}\sqrt{x})
derivative of 4e^{4x}cos(5x)	derivative\:4e^{4x}\cos(5x)
taylor 1/(1-x-x^2),0	taylor\:\frac{1}{1-x-x^{2}},0
sum from n=0 to infinity of 4546644	\sum\:_{n=0}^{\infty\:}4546644
limit as x approaches 3 of (x^x+x)^x	\lim\:_{x\to\:3}((x^{x}+x)^{x})
(ln(x/3))^'	(\ln(\frac{x}{3}))^{\prime\:}
derivative of x^3(x-7)^2	derivative\:x^{3}(x-7)^{2}
tangent of y=x^2+3	tangent\:y=x^{2}+3
(\partial)/(\partial y)(sqrt(41-x^2-4y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{41-x^{2}-4y^{2}})
y^{''}+y/a =0	y^{\prime\:\prime\:}+\frac{y}{a}=0
integral of 1/(x^3+x^2+x+1)	\int\:\frac{1}{x^{3}+x^{2}+x+1}dx
integral from 0 to 1 of pi(x^2-x^4)	\int\:_{0}^{1}π(x^{2}-x^{4})dx
(\partial)/(\partial x)(y*arcsin(x/y))	\frac{\partial\:}{\partial\:x}(y\cdot\:\arcsin(\frac{x}{y}))
derivative of sqrt(6t^2-t)	derivative\:\sqrt{6t^{2}-t}
derivative of f(x)=x^2tan(x)	derivative\:f(x)=x^{2}\tan(x)
integral of 1/(x^2+x-1)	\int\:\frac{1}{x^{2}+x-1}dx
integral from 1 to 4 of 4/(x^2+4x+4)	\int\:_{1}^{4}\frac{4}{x^{2}+4x+4}dx
limit as x approaches 0 of-2	\lim\:_{x\to\:0}(-2)
integral of xIn(x)	\int\:xIn(x)dx
derivative of (2000x/(4x+75))	\frac{d}{dx}(\frac{2000x}{4x+75})
f(x)=6xarcsin(x)	f(x)=6x\arcsin(x)
integral of sin^2((5x)/2)	\int\:\sin^{2}(\frac{5x}{2})dx
(2x+1)y^'+2y=4x	(2x+1)y^{\prime\:}+2y=4x
derivative of 1-sec^2(x)	\frac{d}{dx}(1-\sec^{2}(x))
integral of 1/(5y)	\int\:\frac{1}{5y}dy
y^{''}+y=0,y(pi/3)=0,y^'(pi/3)=8	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=0,y^{\prime\:}(\frac{π}{3})=8
(\partial)/(\partial x)(3x+9x^{17})	\frac{\partial\:}{\partial\:x}(3x+9x^{17})
integral of \sqrt[4]{x^3}+1	\int\:\sqrt[4]{x^{3}}+1dx
integral of 1/(1-tan(x))	\int\:\frac{1}{1-\tan(x)}dx
derivative of (-x^2-9/((x^2-9)^2))	\frac{d}{dx}(\frac{-x^{2}-9}{(x^{2}-9)^{2}})
(x^2+1)y^'+4x(y-1)=0,y(0)=5	(x^{2}+1)y^{\prime\:}+4x(y-1)=0,y(0)=5
integral of xsqrt(16-25x^2)	\int\:x\sqrt{16-25x^{2}}dx
integral from 0 to pi/2 of 3cos(x)	\int\:_{0}^{\frac{π}{2}}3\cos(x)dx
integral of 1/((4x^2-25)^{3/2)}	\int\:\frac{1}{(4x^{2}-25)^{\frac{3}{2}}}dx
integral of sqrt(-4x^2-12x-5)	\int\:\sqrt{-4x^{2}-12x-5}dx
integral of 1/(x^pi)	\int\:\frac{1}{x^{π}}dx
limit as x approaches 0 of (6x)/(3x)	\lim\:_{x\to\:0}(\frac{6x}{3x})
derivative of (ln(x)/(x+1))	\frac{d}{dx}(\frac{\ln(x)}{x+1})
inverse oflaplace ((6s+3))/(s^2)	inverselaplace\:\frac{(6s+3)}{s^{2}}
derivative of ((1+x/(1-x))^2)	\frac{d}{dx}((\frac{1+x}{1-x})^{2})
(d^4)/(dx^4)(1/(3x+1))	\frac{d^{4}}{dx^{4}}(\frac{1}{3x+1})
integral of 2x^3+4x+5	\int\:2x^{3}+4x+5dx
limit as x approaches pi of sin(11/6)	\lim\:_{x\to\:π}(\sin(\frac{11}{6}))
derivative of 1/8 x^4-(32)/(x^3)	derivative\:\frac{1}{8}x^{4}-\frac{32}{x^{3}}
integral from-4pi to 4pi of (sin^2(x)+1)	\int\:_{-4π}^{4π}(\sin^{2}(x)+1)dx
area x^3-11x^2+28x,-x^3+11x^2-28x	area\:x^{3}-11x^{2}+28x,-x^{3}+11x^{2}-28x
y^'=e^{x^2}	y^{\prime\:}=e^{x^{2}}
derivative of e^{ln(ln(2x)})	\frac{d}{dx}(e^{\ln(\ln(2x))})
limit as x approaches 2 of 4/((x-2)^2)	\lim\:_{x\to\:2}(\frac{4}{(x-2)^{2}})
derivative of f(x)=322560(2x+5)	derivative\:f(x)=322560(2x+5)
(d^3)/(dx^3)(sqrt(x+1))	\frac{d^{3}}{dx^{3}}(\sqrt{x+1})
sum from n=0 to infinity of (n!)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{5^{n}}
derivative of 8ysin(x)	\frac{d}{dx}(8y\sin(x))
taylor cos(x),pi	taylor\:\cos(x),π
integral of 8x^3(2x^4+4)	\int\:8x^{3}(2x^{4}+4)dx
derivative of cos(x-1/2)	\frac{d}{dx}(\cos(x)-\frac{1}{2})
integral from 0 to 1 of xe^{3x}	\int\:_{0}^{1}xe^{3x}dx
integral of 9x(1-x)	\int\:9x(1-x)dx
integral from 0 to pi of-cos(x)	\int\:_{0}^{π}-\cos(x)dx
derivative of (x^3)/(x+1)	derivative\:\frac{x^{3}}{x+1}
integral of 18e^x	\int\:18e^{x}dx
integral from 0 to 64 of 5/(x^{2/3)}	\int\:_{0}^{64}\frac{5}{x^{\frac{2}{3}}}dx
integral from-pi/4 to 0 of 8sec^3(x)	\int\:_{-\frac{π}{4}}^{0}8\sec^{3}(x)dx
laplacetransform 15t^3	laplacetransform\:15t^{3}

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