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Popular Calculus Problems

area y=x^3,y=1,x=2	area\:y=x^{3},y=1,x=2
sum from n=0 to infinity of (3^n)/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{4^{n}}
sum from n=1 to infinity of (2n+1)/(n^4)	\sum\:_{n=1}^{\infty\:}\frac{2n+1}{n^{4}}
integral from 1 to infinity of (1/(x^2))	\int\:_{1}^{\infty\:}(\frac{1}{x^{2}})dx
limit as x approaches infinity of f(x)(x)^2	\lim\:_{x\to\:\infty\:}(f(x)(x)^{2})
limit as x approaches-infinity of x^2-1	\lim\:_{x\to\:-\infty\:}(x^{2}-1)
derivative of (x^2+1)(x^2-2x)	derivative\:(x^{2}+1)(x^{2}-2x)
f(x)=(cos(x))/(1-sin(x))	f(x)=\frac{\cos(x)}{1-\sin(x)}
integral of 1/(sqrt(x))+sec^2(x)	\int\:\frac{1}{\sqrt{x}}+\sec^{2}(x)dx
expand (x+a)e^{2x}+b	expand\:(x+a)e^{2x}+b
(\partial)/(\partial y)(6xy-2+10x^2y)	\frac{\partial\:}{\partial\:y}(6xy-2+10x^{2}y)
derivative of ln(sin^3(x^2+7))	\frac{d}{dx}(\ln(\sin^{3}(x^{2}+7)))
y=tan^2(x)	y=\tan^{2}(x)
tangent of y^3+xy^2-61=x+3y^2,\at x=3	tangent\:y^{3}+xy^{2}-61=x+3y^{2},\at\:x=3
integral of (x^2)/(sqrt(2-x))	\int\:\frac{x^{2}}{\sqrt{2-x}}dx
derivative of 2sqrt(1+x^2)	\frac{d}{dx}(2\sqrt{1+x^{2}})
integral of cot(10x)csc^4(10z)	\int\:\cot(10x)\csc^{4}(10z)
implicit xy^2+4xy-4=0	implicit\:xy^{2}+4xy-4=0
integral of x^3-4x^{-2}+5	\int\:x^{3}-4x^{-2}+5dx
integral from 8 to 24 of (x+1/x)	\int\:_{8}^{24}(x+\frac{1}{x})dx
derivative of (4sqrt(t^3))/3+6	derivative\:\frac{4\sqrt{t^{3}}}{3}+6
f(x)=(x^2+1)(x^3-x)(3x^4+2x-1)	f(x)=(x^{2}+1)(x^{3}-x)(3x^{4}+2x-1)
limit as x approaches 0 of ln((-1)/6 x)	\lim\:_{x\to\:0}(\ln(\frac{-1}{6}x))
integral of 5/(3xsqrt(x^2-25))	\int\:\frac{5}{3x\sqrt{x^{2}-25}}dx
integral of (x^2)/(x^4-1)	\int\:\frac{x^{2}}{x^{4}-1}dx
integral of 3/(sqrt(x^3))	\int\:\frac{3}{\sqrt{x^{3}}}dx
integral from-3 to 5 of (y^3-4y)	\int\:_{-3}^{5}(y^{3}-4y)dy
integral from 0 to 2 of 3	\int\:_{0}^{2}3dx
integral from-infinity to 0 of e^{4x}	\int\:_{-\infty\:}^{0}e^{4x}dx
limit as x approaches 0 of e^{3x}	\lim\:_{x\to\:0}(e^{3x})
integral of sqrt((arcsin(x))/(1-x^2))	\int\:\sqrt{\frac{\arcsin(x)}{1-x^{2}}}dx
limit as x approaches 4 of (\|x-4\|)/(x-4)	\lim\:_{x\to\:4}(\frac{\left\|x-4\right\|}{x-4})
integral of e^{-st-t}	\int\:e^{-st-t}dt
derivative of cos(xx^3)	\frac{d}{dx}(\cos(x)x^{3})
integral of (2x+9)^5	\int\:(2x+9)^{5}dx
tangent of f(x)=(4x^2)/(x+3),(1,1)	tangent\:f(x)=\frac{4x^{2}}{x+3},(1,1)
tangent of y=(sqrt(x))/(x+1),(4,0.4)	tangent\:y=\frac{\sqrt{x}}{x+1},(4,0.4)
y^{''}+4y=5csc^2(2t)	y^{\prime\:\prime\:}+4y=5\csc^{2}(2t)
(\partial)/(\partial z)(ysin(z))	\frac{\partial\:}{\partial\:z}(y\sin(z))
derivative of (tan(x)-5)/(sec(x))	derivative\:\frac{\tan(x)-5}{\sec(x)}
integral of sin(3y)	\int\:\sin(3y)dy
derivative of f(x)= 4/(x^4)+10sqrt(x)	derivative\:f(x)=\frac{4}{x^{4}}+10\sqrt{x}
integral of t^2e^{-t/4}	\int\:t^{2}e^{-\frac{t}{4}}dt
integral from-infinity to-1 of e^{-18t}	\int\:_{-\infty\:}^{-1}e^{-18t}dt
derivative of (x-2^2(x-3)^3)	\frac{d}{dx}((x-2)^{2}(x-3)^{3})
integral of 3xsec^2(x)	\int\:3x\sec^{2}(x)dx
integral of (sin^2(x))/(cos^6(x))	\int\:\frac{\sin^{2}(x)}{\cos^{6}(x)}dx
integral of xlog_{10}(x)	\int\:x\log_{10}(x)dx
limit as x approaches pi/4 of sin(x)	\lim\:_{x\to\:\frac{π}{4}}(\sin(x))
f(x)= x/(3x+4ln(x))	f(x)=\frac{x}{3x+4\ln(x)}
implicit (dy)/(dx),y^2=4x	implicit\:\frac{dy}{dx},y^{2}=4x
(\partial)/(\partial y)(xy-y^2)	\frac{\partial\:}{\partial\:y}(xy-y^{2})
(d^2)/(dx^2)((x^2)/(7+6x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{7+6x})
integral of sin(5x)cos^{4/3}(5x)	\int\:\sin(5x)\cos^{\frac{4}{3}}(5x)dx
(\partial)/(\partial x)(e^xxy)	\frac{\partial\:}{\partial\:x}(e^{x}xy)
(dy)/(dx)=(xy+7x-y-7)/(xy-2x+8y-16)	\frac{dy}{dx}=\frac{xy+7x-y-7}{xy-2x+8y-16}
(\partial)/(\partial x)(3x^2y^2+3)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}+3)
integral of x/((x^2-1)^{3/2)}	\int\:\frac{x}{(x^{2}-1)^{\frac{3}{2}}}dx
derivative of 1/(e^{-2x})	\frac{d}{dx}(\frac{1}{e^{-2x}})
taylor ((e^x-e^{-x}))/2	taylor\:\frac{(e^{x}-e^{-x})}{2}
integral of picos(pi)x	\int\:π\cos(π)xdx
integral of (x^5-6x)	\int\:(x^{5}-6x)dx
y^{''}-10y^'+25y=t^{-5}e^{5t}	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=t^{-5}e^{5t}
derivative of x/(x^2-4)	derivative\:\frac{x}{x^{2}-4}
d/(dθ)(1/(2cos(θ)+3sin(θ)))	\frac{d}{dθ}(\frac{1}{2\cos(θ)+3\sin(θ)})
derivative of sin(sin(2x))	\frac{d}{dx}(\sin(\sin(2x)))
integral of-2	\int\:-2dx
integral of (3x^5-5x+6)	\int\:(3x^{5}-5x+6)dx
inverse oflaplace (s+1)/(s^2(s^2+1))	inverselaplace\:\frac{s+1}{s^{2}(s^{2}+1)}
limit as x approaches 1 of (\|x-1\|)/(x-1)	\lim\:_{x\to\:1}(\frac{\left\|x-1\right\|}{x-1})
(dy)/(dx)=136x-xy	\frac{dy}{dx}=136x-xy
(dy)/(dx)=(2x)/(1+2y)	\frac{dy}{dx}=\frac{2x}{1+2y}
x^{''}-3x^'-10x=20t	x^{\prime\:\prime\:}-3x^{\prime\:}-10x=20t
(1-x)y^{''}+xy^'-y=(x-1)^2e^{-x}	(1-x)y^{\prime\:\prime\:}+xy^{\prime\:}-y=(x-1)^{2}e^{-x}
integral from 1 to infinity of x^{-1/9}	\int\:_{1}^{\infty\:}x^{-\frac{1}{9}}dx
inverse oflaplace 2/(s(s+2)+2)	inverselaplace\:\frac{2}{s(s+2)+2}
derivative of y= 23/5 x-12	derivative\:y=\frac{23}{5}x-12
derivative of f(x)=\sqrt[8]{x}	derivative\:f(x)=\sqrt[8]{x}
derivative of-5e^{-5x}	\frac{d}{dx}(-5e^{-5x})
tangent of f(x)= 1/(x^6),(1,1)	tangent\:f(x)=\frac{1}{x^{6}},(1,1)
derivative of 1/(4x^3-5/(2x))	\frac{d}{dx}(\frac{1}{4x^{3}}-\frac{5}{2x})
(\partial)/(\partial x)(x^2+(y-1)^2+z^2)	\frac{\partial\:}{\partial\:x}(x^{2}+(y-1)^{2}+z^{2})
area x,x^{2.42},[0.99,1]	area\:x,x^{2.42},[0.99,1]
derivative of (2x/(x+8))	\frac{d}{dx}(\frac{2x}{x+8})
derivative of y=5csc(x)+6cos(x)	derivative\:y=5\csc(x)+6\cos(x)
area y=sin(x),y=5x,x= pi/2 ,x=pi	area\:y=\sin(x),y=5x,x=\frac{π}{2},x=π
integral of 1/(2sqrt(x+3)+x)	\int\:\frac{1}{2\sqrt{x+3}+x}dx
xdy+(y-3xy)dx=0	xdy+(y-3xy)dx=0
sum from n=1 to infinity of (ln(n))/(5n)	\sum\:_{n=1}^{\infty\:}\frac{\ln(n)}{5n}
(\partial)/(\partial x)(\sqrt[3]{1/x})	\frac{\partial\:}{\partial\:x}(\sqrt[3]{\frac{1}{x}})
limit as x approaches 1 of-cos(1/(x-1))	\lim\:_{x\to\:1}(-\cos(\frac{1}{x-1}))
(\partial)/(\partial x)(6e^xcos(yz))	\frac{\partial\:}{\partial\:x}(6e^{x}\cos(yz))
derivative of 5+sin(45)	\frac{d}{dx}(5+\sin(45))
limit as x approaches 0+of (x^2)/5-7/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{5}-\frac{7}{x})
limit as x approaches infinity of (log_{2}(x))/(\sqrt[3]{x)}	\lim\:_{x\to\:\infty\:}(\frac{\log_{2}(x)}{\sqrt[3]{x}})
limit as x approaches 0 of 2+5/(x^2)	\lim\:_{x\to\:0}(2+\frac{5}{x^{2}})
derivative of y=((8x^2)/(2-x))^3	derivative\:y=(\frac{8x^{2}}{2-x})^{3}
area cos(x),sin(x),[0, pi/2 ]	area\:\cos(x),\sin(x),[0,\frac{π}{2}]
integral of x^5sqrt(9x^2-1)	\int\:x^{5}\sqrt{9x^{2}-1}dx
(\partial)/(\partial y)(3x^2y+cos(y))	\frac{\partial\:}{\partial\:y}(3x^{2}y+\cos(y))

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