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Popular Calculus Problems

integral of (x^2-x+1)/x	\int\:\frac{x^{2}-x+1}{x}dx
(x-9)y^'+y=x^2-10	(x-9)y^{\prime\:}+y=x^{2}-10
integral of 1/(x^2+xsqrt(x))	\int\:\frac{1}{x^{2}+x\sqrt{x}}dx
limit as x approaches 7 of 2	\lim\:_{x\to\:7}(2)
tangent of f(x)= 5/x ,\at x=3	tangent\:f(x)=\frac{5}{x},\at\:x=3
integral of 36x(9x^2-7)^3	\int\:36x(9x^{2}-7)^{3}dx
integral of 5tan(5x)	\int\:5\tan(5x)dx
limit as x approaches 4-of x+1	\lim\:_{x\to\:4-}(x+1)
(\partial)/(\partial x)(x^2+y^2-2x)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-2x)
derivative of-4sin^2(x)	\frac{d}{dx}(-4\sin^{2}(x))
integral of 16cos^2(x)	\int\:16\cos^{2}(x)dx
y^{''}-4y=((e^{2x}))/((x))	y^{\prime\:\prime\:}-4y=\frac{(e^{2x})}{(x)}
limit as x approaches-3 of-x^2-x+4	\lim\:_{x\to\:-3}(-x^{2}-x+4)
limit as x approaches 0 of \sqrt[x]{2}	\lim\:_{x\to\:0}(\sqrt[x]{2})
derivative of (2x-1)ln(2x-1)	derivative\:(2x-1)\ln(2x-1)
implicit (dy)/(dx),y^5=x^8	implicit\:\frac{dy}{dx},y^{5}=x^{8}
integral of x(5^{-x^2})	\int\:x(5^{-x^{2}})dx
integral of 1-sqrt(x)	\int\:1-\sqrt{x}dx
integral of (3x^4-4x^3+6x^2-x/2+3)	\int\:(3x^{4}-4x^{3}+6x^{2}-\frac{x}{2}+3)dx
integral of 8tan(x)sin(y)cos(y)	\int\:8\tan(x)\sin(y)\cos(y)dx
derivative of (2x^2-7^5-(1+4x^3)^5)	\frac{d}{dx}((2x^{2}-7)^{5}-(1+4x^{3})^{5})
derivative of (3x)/(e^x)	derivative\:\frac{3x}{e^{x}}
(x*e^x)^'	(x\cdot\:e^{x})^{\prime\:}
derivative of-xcos(3x)	\frac{d}{dx}(-x\cos(3x))
integral of 2/(x^3sqrt(x^4-25))	\int\:\frac{2}{x^{3}\sqrt{x^{4}-25}}dx
integral of 1/(x^3sqrt(x^2-4))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-4}}dx
integral of 9x^2-30x+15	\int\:9x^{2}-30x+15dx
(\partial)/(\partial x)(x*sin(y-z))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(y-z))
d/(dt)((\sqrt[3]{t})/5)	\frac{d}{dt}(\frac{\sqrt[3]{t}}{5})
(\partial)/(\partial x)(6-(x^2+y^2)^{1/5})	\frac{\partial\:}{\partial\:x}(6-(x^{2}+y^{2})^{\frac{1}{5}})
(\partial)/(\partial y)(x*e^{xy+1})	\frac{\partial\:}{\partial\:y}(x\cdot\:e^{xy+1})
derivative of y=x^{-1}	derivative\:y=x^{-1}
y^'= 1/(xy)	y^{\prime\:}=\frac{1}{xy}
tangent of f(x)=8x^2-3,\at x=3	tangent\:f(x)=8x^{2}-3,\at\:x=3
derivative of f(0)=(cos(x))/(x^2-1)	derivative\:f(0)=\frac{\cos(x)}{x^{2}-1}
integral from 1 to 4 of 7e^{sqrt(x)}	\int\:_{1}^{4}7e^{\sqrt{x}}dx
sum from n=1 to infinity of (2^n)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{2^{n}}{10^{n}}
(\partial ^2)/(\partial y^2)(xy^{10}+x^2+y^4)	\frac{\partial\:^{2}}{\partial\:y^{2}}(xy^{10}+x^{2}+y^{4})
derivative of f(x)=x^{-1/2}+x^{1/2}	derivative\:f(x)=x^{-\frac{1}{2}}+x^{\frac{1}{2}}
inverse oflaplace 1/(s^3+s^2+s)	inverselaplace\:\frac{1}{s^{3}+s^{2}+s}
derivative of y=x^3-sqrt(x)	derivative\:y=x^{3}-\sqrt{x}
derivative of f(x)=cos(sqrt(4t+12))	derivative\:f(x)=\cos(\sqrt{4t+12})
limit as x approaches 0 of (y^{1-x})/(1-x)	\lim\:_{x\to\:0}(\frac{y^{1-x}}{1-x})
y^{''}-6y^'+2y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}-6y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=1
limit as x approaches 5 of sqrt(x^2+4)	\lim\:_{x\to\:5}(\sqrt{x^{2}+4})
integral of (3x^2-3)/(x^3-3x)	\int\:\frac{3x^{2}-3}{x^{3}-3x}dx
3x(dy)/(dx)+5y=10	3x\frac{dy}{dx}+5y=10
integral of tan^6(9x)sec^4(9x)	\int\:\tan^{6}(9x)\sec^{4}(9x)dx
integral from 0 to 3 of pi(2sqrt(5y))^2	\int\:_{0}^{3}π(2\sqrt{5y})^{2}dy
normal of y=F4x-x^2,(1,3)	normal\:y=F4x-x^{2},(1,3)
integral of sin^3(1-2x)cos^3(1-2x)	\int\:\sin^{3}(1-2x)\cos^{3}(1-2x)dx
derivative of 3x-4x^{9/10}	\frac{d}{dx}(3x-4x^{\frac{9}{10}})
tangent of y=(9x^2-6x+2)(1+2x),\at x=1	tangent\:y=(9x^{2}-6x+2)(1+2x),\at\:x=1
derivative of asqrt(1+x)	\frac{d}{dx}(a\sqrt{1+x})
area sqrt(x)+9,0.25x+9	area\:\sqrt{x}+9,0.25x+9
derivative of \|3x-4\|	\frac{d}{dx}(\left\|3x-4\right\|)
integral of (x^2)/(sqrt(10-3x^3))	\int\:\frac{x^{2}}{\sqrt{10-3x^{3}}}dx
integral of (90x^2sin(2+6x^3))	\int\:(90x^{2}\sin(2+6x^{3}))dx
derivative of sqrt((3x+7/(5+2x)))	\frac{d}{dx}(\sqrt{\frac{3x+7}{5+2x}})
derivative of (ln(x+1)^2-e^{x^2})	\frac{d}{dx}((\ln(x+1))^{2}-e^{x^{2}})
integral of \|4y+1\|	\int\:\left\|4y+1\right\|dy
y^'+7y=t+e^{-6t}	y^{\prime\:}+7y=t+e^{-6t}
2xdx+dy=0	2xdx+dy=0
sum from n=0 to infinity of 5(0.7)^{n-1}	\sum\:_{n=0}^{\infty\:}5(0.7)^{n-1}
integral of e^{4x}	\int\:e^{4x}dx
integral of ((-1)^k)/((2k+1)!)(2x)^{2k}	\int\:\frac{(-1)^{k}}{(2k+1)!}(2x)^{2k}dx
(dx)/(dt)=x+t	\frac{dx}{dt}=x+t
derivative of 3/(sqrt((45+36)^3))	derivative\:\frac{3}{\sqrt{(45+36)^{3}}}
derivative of e^{x^7}	derivative\:e^{x^{7}}
derivative of x 2/3	\frac{d}{dx}(x\frac{2}{3})
integral of 1/(xsqrt(4x^2-9))	\int\:\frac{1}{x\sqrt{4x^{2}-9}}dx
limit as x approaches 0 of (e^x-1)/(x^5)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{x^{5}})
(\partial)/(\partial x)(ln(x^2+y^2+1))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{2}+1))
(\partial)/(\partial y)(ln(x+z))	\frac{\partial\:}{\partial\:y}(\ln(x+z))
derivative of y=2x-4	derivative\:y=2x-4
derivative of 1/(sqrt(x^2+5))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}+5}})
limit as x approaches 1 of (x^5-1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{5}-1}{x-1})
derivative of f(x)=xsin(2^x)	derivative\:f(x)=x\sin(2^{x})
1/x e^ytan(y)y^'=e^{x+y}	\frac{1}{x}e^{y}\tan(y)y^{\prime\:}=e^{x+y}
(\partial)/(\partial y)((4x)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{4x}{x^{2}+y^{2}})
integral of 1/2 (cos(x))^2	\int\:\frac{1}{2}(\cos(x))^{2}dx
tangent of f(x)=(40)/x ,(1,40)	tangent\:f(x)=\frac{40}{x},(1,40)
integral of ((x+1)/(sqrt(x)))	\int\:(\frac{x+1}{\sqrt{x}})dx
integral of 1/2 x^5	\int\:\frac{1}{2}x^{5}dx
limit as x approaches pi/2+of 2e^{tan(x)}	\lim\:_{x\to\:\frac{π}{2}+}(2e^{\tan(x)})
tangent of f(x)=3x^4-8x^2,(-1,5)	tangent\:f(x)=3x^{4}-8x^{2},(-1,5)
(\partial)/(\partial x)(-3xyln(xy))	\frac{\partial\:}{\partial\:x}(-3xy\ln(xy))
(\partial)/(\partial x)((xy^2)/(z^3))	\frac{\partial\:}{\partial\:x}(\frac{xy^{2}}{z^{3}})
y^{''}=-y	y^{\prime\:\prime\:}=-y
integral of x-7	\int\:x-7dx
limit as x approaches+0 of (e^{x^2}-1)/x	\lim\:_{x\to\:+0}(\frac{e^{x^{2}}-1}{x})
derivative of (x^2+25/x)	\frac{d}{dx}(\frac{x^{2}+25}{x})
(\partial)/(\partial z)(ln(1+z^2))	\frac{\partial\:}{\partial\:z}(\ln(1+z^{2}))
integral of-(6000)/((3x+50)^2)	\int\:-\frac{6000}{(3x+50)^{2}}dx
limit as x approaches 15 of sqrt(2)	\lim\:_{x\to\:15}(\sqrt{2})
taylor e^{2x},1	taylor\:e^{2x},1
(\partial)/(\partial x)(x^2-4y)	\frac{\partial\:}{\partial\:x}(x^{2}-4y)
y(dy)/(dx)-e^{y^2}xcos(x)=0	y\frac{dy}{dx}-e^{y^{2}}\cdot\:x\cdot\:\cos(x)=0
derivative of-(50/(x^3)+5/(x^2))	\frac{d}{dx}(-\frac{50}{x^{3}}+\frac{5}{x^{2}})
integral of 4x^2sin(2x)	\int\:4x^{2}\sin(2x)dx

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