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Popular Calculus Problems

integral of (x^2+3)/(\sqrt[3]{x+2)}	\int\:\frac{x^{2}+3}{\sqrt[3]{x+2}}dx
(\partial)/(\partial x)(10(11x-3y+12)^5)	\frac{\partial\:}{\partial\:x}(10(11x-3y+12)^{5})
derivative of x-3/2	\frac{d}{dx}(x-\frac{3}{2})
integral of csc^2(y) 1/(1+cot(y))	\int\:\csc^{2}(y)\frac{1}{1+\cot(y)}dy
derivative of (x^2/(y^3))	\frac{d}{dx}(\frac{x^{2}}{y^{3}})
limit as x approaches 2 of x^2+x+2	\lim\:_{x\to\:2}(x^{2}+x+2)
limit as x approaches 1 of sin(x)	\lim\:_{x\to\:1}(\sin(x))
limit as r approaches 9 of (4r-3)/(11)	\lim\:_{r\to\:9}(\frac{4r-3}{11})
xy^'-2y=5x^2	xy^{\prime\:}-2y=5x^{2}
integral of (x^2)/(sqrt(x^6+25))	\int\:\frac{x^{2}}{\sqrt{x^{6}+25}}dx
limit as x approaches 0 of x^2cos(x^5)	\lim\:_{x\to\:0}(x^{2}\cos(x^{5}))
limit as x approaches 1 of 1/(x^2)-1/x	\lim\:_{x\to\:1}(\frac{1}{x^{2}}-\frac{1}{x})
derivative of-1/(1+x)	\frac{d}{dx}(-\frac{1}{1+x})
derivative of (x^{1/2}*(x^2+x-4))	\frac{d}{dx}((x^{\frac{1}{2}})\cdot\:(x^{2}+x-4))
derivative of x^3+bx^2+cx+d	\frac{d}{dx}(x^{3}+bx^{2}+cx+d)
(\partial)/(\partial y)(sin(xy)+xsin(y))	\frac{\partial\:}{\partial\:y}(\sin(xy)+x\sin(y))
limit as x approaches-1-of (x+2x^3)^4	\lim\:_{x\to\:-1-}((x+2x^{3})^{4})
sum from n=0 to infinity of (5/5)^n	\sum\:_{n=0}^{\infty\:}(\frac{5}{5})^{n}
xy^'+5y=x^3-x	xy^{\prime\:}+5y=x^{3}-x
integral of (x+1)/(x^2-2x)	\int\:\frac{x+1}{x^{2}-2x}dx
(\partial)/(\partial s)(s*cos(t))	\frac{\partial\:}{\partial\:s}(s\cdot\:\cos(t))
f(x)=6cos(2x)	f(x)=6\cos(2x)
derivative of f(x)=(x^3-8)/(x^2+3)	derivative\:f(x)=\frac{x^{3}-8}{x^{2}+3}
tangent of f(x)=3x^2+2x-10,\at x=1	tangent\:f(x)=3x^{2}+2x-10,\at\:x=1
derivative of f(t)=e^{4tsin(2t)}	derivative\:f(t)=e^{4t\sin(2t)}
integral of (sin(2x))/(x^2)	\int\:\frac{\sin(2x)}{x^{2}}dx
integral of x^3ln(6x)	\int\:x^{3}\ln(6x)dx
derivative of sqrt(x)cos(sqrt(x))	\frac{d}{dx}(\sqrt{x}\cos(\sqrt{x}))
integral of (y-1)/(y+4)	\int\:\frac{y-1}{y+4}dy
limit as x approaches 3 of 6x^2	\lim\:_{x\to\:3}(6x^{2})
integral of 8sec^3(6x)	\int\:8\sec^{3}(6x)dx
(\partial)/(\partial x)(3e^{2x}-5ln(y)+7)	\frac{\partial\:}{\partial\:x}(3e^{2x}-5\ln(y)+7)
integral from 2 to 7 of x	\int\:_{2}^{7}xdx
(dy)/(dx)=((3y+2)/(5x+4))^2	\frac{dy}{dx}=(\frac{3y+2}{5x+4})^{2}
integral of ln(sqrt(2x))	\int\:\ln(\sqrt{2x})dx
(\partial)/(\partial x)(sin(4x))	\frac{\partial\:}{\partial\:x}(\sin(4x))
integral from 0 to 3 of (3-x)	\int\:_{0}^{3}(3-x)dx
derivative of 4x^4sqrt(25-x^2)	\frac{d}{dx}(4x^{4}\sqrt{25-x^{2}})
(\partial)/(\partial x)(4x^2y+6xy^2)	\frac{\partial\:}{\partial\:x}(4x^{2}y+6xy^{2})
derivative of (7x/(x^2+4))	\frac{d}{dx}(\frac{7x}{x^{2}+4})
derivative of 1/6 x^3+1/(2x)	derivative\:\frac{1}{6}x^{3}+\frac{1}{2x}
derivative of sqrt(4+3{f)(x})	\frac{d}{dx}(\sqrt{4+3{f}(x)})
limit as x approaches 0+of ln(9/(x^3))	\lim\:_{x\to\:0+}(\ln(\frac{9}{x^{3}}))
derivative of cos^2(ln(e^{2x+1}(-2x)))	\frac{d}{dx}(\cos^{2}(\ln(e^{2x+1}(-2x))))
laplacetransform e^{4t}	laplacetransform\:e^{4t}
limit as x approaches 0 of (2/x)^x	\lim\:_{x\to\:0}((\frac{2}{x})^{x})
limit as x approaches 4+of 4sqrt(x-4)	\lim\:_{x\to\:4+}(4\sqrt{x-4})
area f(x)=2x^3+3x^2+5x,-4,3	area\:f(x)=2x^{3}+3x^{2}+5x,-4,3
(\partial)/(\partial x)(e^{3x}sin(3y))	\frac{\partial\:}{\partial\:x}(e^{3x}\sin(3y))
derivative of c_{1}e^x+c_{2}xe^x	\frac{d}{dx}(c_{1}e^{x}+c_{2}xe^{x})
sum from n=0 to infinity of 1/(10^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{10^{n}}
y^'+7y=t+e^{-2t}	y^{\prime\:}+7y=t+e^{-2t}
limit as x approaches 0+of x^3+3x+2	\lim\:_{x\to\:0+}(x^{3}+3x+2)
integral of 2/(x^2+2x+2)	\int\:\frac{2}{x^{2}+2x+2}dx
limit as x approaches 1-of x^2-1	\lim\:_{x\to\:1-}(x^{2}-1)
limit as x approaches 1 of (x-1)/(x^2-1)	\lim\:_{x\to\:1}(\frac{x-1}{x^{2}-1})
derivative of x^3(ln(x)^{cos(x)})	\frac{d}{dx}(x^{3}(\ln(x))^{\cos(x)})
integral of y^{-4}	\int\:y^{-4}dy
tangent of f(x)= 3/((x+5)^2),\at x= 3/16	tangent\:f(x)=\frac{3}{(x+5)^{2}},\at\:x=\frac{3}{16}
(\partial)/(\partial y)((5x)/(6y))	\frac{\partial\:}{\partial\:y}(\frac{5x}{6y})
(cot(x))^'	(\cot(x))^{\prime\:}
(\partial)/(\partial x)(tan(3x-4y))	\frac{\partial\:}{\partial\:x}(\tan(3x-4y))
integral of 3/(u^2+2)	\int\:\frac{3}{u^{2}+2}du
derivative of f(x)=(2x-x^2)^3	derivative\:f(x)=(2x-x^{2})^{3}
derivative of sec^4(x-tan^4(x))	\frac{d}{dx}(\sec^{4}(x)-\tan^{4}(x))
y^'=3-(2y)	y^{\prime\:}=3-(2y)
(\partial)/(\partial y)(ln(x^2+y^3))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{3}))
simplify (x-5)/(sqrt(x))	simplify\:\frac{x-5}{\sqrt{x}}
derivative of (1+2xsqrt(y))	\frac{d}{dx}((1+2x)\sqrt{y})
integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}	\int\:_{4}^{9}\frac{1}{2}y^{\frac{1}{2}}+\frac{1}{2}y^{-\frac{1}{2}}dy
derivative of a(2e^{-2x}x-2e^{-2x}x^2)	\frac{d}{dx}(a(2e^{-2x}x-2e^{-2x}x^{2}))
integral from-2 to 4 of x+2	\int\:_{-2}^{4}x+2dx
(\partial)/(\partial y)(-y/(y^2+x^2))	\frac{\partial\:}{\partial\:y}(-\frac{y}{y^{2}+x^{2}})
y^{''}+5y^'+4y=2te^{3t}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=2te^{3t}
integral from 0 to 6 of 36-x^2	\int\:_{0}^{6}36-x^{2}dx
limit as x approaches 0+of ln(ln(x))	\lim\:_{x\to\:0+}(\ln(\ln(x)))
(dy)/(dx)= 1/(sec^2(y))	\frac{dy}{dx}=\frac{1}{\sec^{2}(y)}
derivative of (x^4+2/(ln(x)))	\frac{d}{dx}(\frac{x^{4}+2}{\ln(x)})
integral of x/(e^{4x)}	\int\:\frac{x}{e^{4x}}dx
sum from n=1 to infinity of 2/(9^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{9^{n}}
tangent of 3x-2x^2	tangent\:3x-2x^{2}
limit as x approaches 0 of (e^{-1/x})^x	\lim\:_{x\to\:0}((e^{-\frac{1}{x}})^{x})
(dy)/(dt)+ty=ty^2	\frac{dy}{dt}+ty=ty^{2}
integral of xe^{2xy}	\int\:xe^{2xy}dy
integral of x*1/x	\int\:x\cdot\:\frac{1}{x}dx
integral of x^3+e^x+2	\int\:x^{3}+e^{x}+2dx
sum from n=1 to infinity of 1/((-1)^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{(-1)^{n}}
(\partial)/(\partial y)(3x^2y+4xy^2)	\frac{\partial\:}{\partial\:y}(3x^{2}y+4xy^{2})
integral of e^xsqrt(8+e^x)	\int\:e^{x}\sqrt{8+e^{x}}dx
y^'=((e^{(x-y)}))/(1+e^x)	y^{\prime\:}=\frac{(e^{(x-y)})}{1+e^{x}}
integral of e^{-x/(10)}	\int\:e^{-\frac{x}{10}}dx
derivative of 20-2x	\frac{d}{dx}(20-2x)
derivative of (x^4/8 ln(x)-(x^4)/(32))	\frac{d}{dx}(\frac{x^{4}}{8}\ln(x)-\frac{x^{4}}{32})
tangent of y= 8/(x+1)	tangent\:y=\frac{8}{x+1}
limit as x approaches 0 of x*e^{1/x}	\lim\:_{x\to\:0}(x\cdot\:e^{\frac{1}{x}})
derivative of y=(x^4-6x)e^x	derivative\:y=(x^{4}-6x)e^{x}
(\partial)/(\partial x)((2x)/(x^2+y^2+16))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}+y^{2}+16})
derivative of (cos(2x)/x)	\frac{d}{dx}(\frac{\cos(2x)}{x})
derivative of 3x^5sqrt(x)+7/(x^3sqrt(x))	derivative\:3x^{5}\sqrt{x}+\frac{7}{x^{3}\sqrt{x}}
(\partial)/(\partial x)(ln(((x+y))/(x-y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{(x+y)}{x-y}))

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