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Popular Calculus Problems
limit as x approaches 7+of 1/((x-7)^2)
\lim\:_{x\to\:7+}(\frac{1}{(x-7)^{2}})
derivative of (9x^2)/(sqrt(6+x^3))
derivative\:\frac{9x^{2}}{\sqrt{6+x^{3}}}
integral of 1/(xsqrt(-1+x^2))
\int\:\frac{1}{x\sqrt{-1+x^{2}}}dx
integral from 2 to 4 of 4x
\int\:_{2}^{4}4xdx
limit as x approaches (5pi)/2+of sec(x)
\lim\:_{x\to\:\frac{5π}{2}+}(\sec(x))
integral of ((cos(x))/(1-cos^2(x)))
\int\:(\frac{\cos(x)}{1-\cos^{2}(x)})dx
(\partial)/(\partial y)(sqrt(x)ln(y))
\frac{\partial\:}{\partial\:y}(\sqrt{x}\ln(y))
derivative of f(x)=-8
derivative\:f(x)=-8
derivative of \sqrt[7]{t}
derivative\:\sqrt[7]{t}
derivative of \sqrt[3]{(2x+3)/(3x-5)}
derivative\:\sqrt[3]{\frac{2x+3}{3x-5}}
derivative of f(x)=sin(9ln(x))
derivative\:f(x)=\sin(9\ln(x))
y^{''}+4y=sin(x),y(0)=1,y^'(0)=4
y^{\prime\:\prime\:}+4y=\sin(x),y(0)=1,y^{\prime\:}(0)=4
integral of 4e^{x^2}
\int\:4e^{x^{2}}dx
integral from 0 to pi/4 of 2sec^2(x)
\int\:_{0}^{\frac{π}{4}}2\sec^{2}(x)dx
integral of (x+3)/(2x^3-8x)
\int\:\frac{x+3}{2x^{3}-8x}dx
tangent of y=2xtan(x),\at x=pi
tangent\:y=2x\tan(x),\at\:x=π
limit as x approaches 0 of (2x-1)/x
\lim\:_{x\to\:0}(\frac{2x-1}{x})
integral of (sin(2x))/(2cos^2(x))
\int\:\frac{\sin(2x)}{2\cos^{2}(x)}dx
derivative of-32sin(2x)
\frac{d}{dx}(-32\sin(2x))
area 1+x-x^2-x^3,1-x,[-2,1]
area\:1+x-x^{2}-x^{3},1-x,[-2,1]
(\partial)/(\partial y)(cos(yz))
\frac{\partial\:}{\partial\:y}(\cos(yz))
(x+2)sin(y)+(xcos(y))y^'=0
(x+2)\sin(y)+(x\cos(y))y^{\prime\:}=0
limit as x approaches 0+of ln(0)-1/x
\lim\:_{x\to\:0+}(\ln(0)-\frac{1}{x})
integral from-1 to 3 of 1/(x^2)
\int\:_{-1}^{3}\frac{1}{x^{2}}dx
y^{''}-12y^'+38y=0
y^{\prime\:\prime\:}-12y^{\prime\:}+38y=0
integral of 1/2 cos^2(3θ)
\int\:\frac{1}{2}\cos^{2}(3θ)dθ
integral of r^2(r^3-4)^7
\int\:r^{2}(r^{3}-4)^{7}dr
(dy)/(dx)+2y=2x
\frac{dy}{dx}+2y=2x
y^'+1/x y=xy^2
y^{\prime\:}+\frac{1}{x}y=xy^{2}
derivative of xy+x
derivative\:xy+x
tangent of f(x)= 6/(x^2),(1,6)
tangent\:f(x)=\frac{6}{x^{2}},(1,6)
derivative of (f(x(3x))^2-4)
\frac{d}{dx}((f(x)(3x))^{2}-4)
integral from pi/3 to pi of sin(x)
\int\:_{\frac{π}{3}}^{π}\sin(x)dx
integral of (x^4-5x^2+2x)/(5x^2)
\int\:\frac{x^{4}-5x^{2}+2x}{5x^{2}}dx
derivative of 6+4/x+6/(x^2)
derivative\:6+\frac{4}{x}+\frac{6}{x^{2}}
integral of 4^x(4^x+1)^3
\int\:4^{x}(4^{x}+1)^{3}dx
slope ofintercept (-1/2 ,1),(-2, 1/2)
slopeintercept\:(-\frac{1}{2},1),(-2,\frac{1}{2})
derivative of sin(x^3+2)
\frac{d}{dx}(\sin(x^{3}+2))
(\partial)/(\partial x)(4x-2)
\frac{\partial\:}{\partial\:x}(4x-2)
limit as x approaches 0+of tan^x(3x)
\lim\:_{x\to\:0+}(\tan^{x}(3x))
(dy)/(dt)=3t+y/(2t)
\frac{dy}{dt}=3t+\frac{y}{2t}
integral of sqrt(4-y)
\int\:\sqrt{4-y}dy
implicit x^2+y^2=49
implicit\:x^{2}+y^{2}=49
y^{''}+4y=3sin(2t),y(0)=2,y^'(0)=-1
y^{\prime\:\prime\:}+4y=3\sin(2t),y(0)=2,y^{\prime\:}(0)=-1
derivative of (x-3xsqrt(x)/(sqrt(x)))
\frac{d}{dx}(\frac{x-3x\sqrt{x}}{\sqrt{x}})
derivative of (2x/(sqrt(3x-1)))
\frac{d}{dx}(\frac{2x}{\sqrt{3x-1}})
derivative of 1/(4x^2+6x)
\frac{d}{dx}(\frac{1}{4x^{2}+6x})
derivative of sqrt((4+x^2)/(4-x))
derivative\:\sqrt{\frac{4+x^{2}}{4-x}}
tangent of f(x)=(12x-8)^{1/2},\at x=2
tangent\:f(x)=(12x-8)^{\frac{1}{2}},\at\:x=2
(dy)/(dx)=7xy^2
\frac{dy}{dx}=7xy^{2}
integral from 0 to 2 of 1/(x^2-1)
\int\:_{0}^{2}\frac{1}{x^{2}-1}dx
(\partial)/(\partial x)(3x^2y+2y)
\frac{\partial\:}{\partial\:x}(3x^{2}y+2y)
area x=-5,x=1,y=2x^2+12,y=0
area\:x=-5,x=1,y=2x^{2}+12,y=0
integral from 1 to 2 of xe^x
\int\:_{1}^{2}xe^{x}dx
derivative of f(x)=5^{sin(x)}
derivative\:f(x)=5^{\sin(x)}
integral from 1 to e of ln(11x)
\int\:_{1}^{e}\ln(11x)dx
(\partial)/(\partial x)(xln(y))
\frac{\partial\:}{\partial\:x}(x\ln(y))
integral of (2x^2+1)/(x^2)
\int\:\frac{2x^{2}+1}{x^{2}}dx
area x^5+5,x+5
area\:x^{5}+5,x+5
integral of 5^{x^2}
\int\:5^{x^{2}}dx
derivative of 6xsin(pix)
\frac{d}{dx}(6x\sin(πx))
derivative of sqrt(2-1/x)
\frac{d}{dx}(\sqrt{2-\frac{1}{x}})
integral of x/(sqrt(36-x^2))
\int\:\frac{x}{\sqrt{36-x^{2}}}dx
integral of (5x^3+5x)/(x-1)
\int\:\frac{5x^{3}+5x}{x-1}dx
d/(dt)(\sqrt[3]{t})
\frac{d}{dt}(\sqrt[3]{t})
integral of x-1/2 sin(2x)
\int\:x-\frac{1}{2}\sin(2x)dx
derivative of e^{(2x})
\frac{d}{dx}(e^{(2x)})
derivative of 5x^3ln(x)
\frac{d}{dx}(5x^{3}\ln(x))
derivative of \sqrt[6]{x-x^2}
\frac{d}{dx}(\sqrt[6]{x-x^{2}})
y^'+y=e^t+11
y^{\prime\:}+y=e^{t}+11
inverse oflaplace s^2+7s+12
inverselaplace\:s^{2}+7s+12
(dy)/(dx)=((5y^4-2xy))/(x^2)
\frac{dy}{dx}=\frac{(5y^{4}-2xy)}{x^{2}}
derivative of 12x^3-36x^2
\frac{d}{dx}(12x^{3}-36x^{2})
(\partial)/(\partial x)(e^{-5x^2-4y^2})
\frac{\partial\:}{\partial\:x}(e^{-5x^{2}-4y^{2}})
derivative of f(x)=ln(x/(x^2+1))
derivative\:f(x)=\ln(\frac{x}{x^{2}+1})
limit as x approaches 3-of e^{2/(x-3)}
\lim\:_{x\to\:3-}(e^{\frac{2}{x-3}})
integral of 5^tsin(5^t)
\int\:5^{t}\sin(5^{t})dt
integral of sqrt(x)(ln^2(x))
\int\:\sqrt{x}(\ln^{2}(x))dx
sum from n=1 to infinity of (n/(n+10))^n
\sum\:_{n=1}^{\infty\:}(\frac{n}{n+10})^{n}
2xy^'=y^2
2xy^{\prime\:}=y^{2}
integral of cos^2(u)
\int\:\cos^{2}(u)du
integral from 0 to 25 of sqrt(x)
\int\:_{0}^{25}\sqrt{x}dx
xy^'=x^3+17x^3y
xy^{\prime\:}=x^{3}+17x^{3}y
d/(dz)(csc(arcsin(z^2)))
\frac{d}{dz}(\csc(\arcsin(z^{2})))
derivative of ln(arctan(8x^3))
\frac{d}{dx}(\ln(\arctan(8x^{3})))
integral of 4e^{9x}
\int\:4e^{9x}dx
tangent of f(x)=x^4-25x^2+144,\at x=1
tangent\:f(x)=x^{4}-25x^{2}+144,\at\:x=1
integral of 1 (y)
\int\:\frac{d}{1}(y)dx
derivative of tan^{1/x}(x)
\frac{d}{dx}(\tan^{\frac{1}{x}}(x))
derivative of (u^{-2}+u^{-3})(u^5-9u^2)
derivative\:(u^{-2}+u^{-3})(u^{5}-9u^{2})
integral of-3ln(x^2-1)
\int\:-3\ln(x^{2}-1)dx
derivative of ln(cos(x^2))
\frac{d}{dx}(\ln(\cos(x^{2})))
integral of sin^2((pix)/6)
\int\:\sin^{2}(\frac{πx}{6})dx
limit as x approaches 1+of x^{2/(1-x)}
\lim\:_{x\to\:1+}(x^{\frac{2}{1-x}})
derivative of 4+sqrt(7x)
derivative\:4+\sqrt{7x}
area y=2x,y=sqrt(x)
area\:y=2x,y=\sqrt{x}
derivative of sec(2x^3)
\frac{d}{dx}(\sec(2x^{3}))
derivative of (x-2/x+ln(x/2))
\frac{d}{dx}(\frac{x-2}{x}+\ln(\frac{x}{2}))
integral from-infinity to 5 of xe^x
\int\:_{-\infty\:}^{5}xe^{x}dx
1/((1+2y^2))y^'=csc(x)
\frac{1}{(1+2y^{2})}y^{\prime\:}=\csc(x)
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