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Popular Calculus Problems

integral from 0 to 5 of 1/(x^2+25)	\int\:_{0}^{5}\frac{1}{x^{2}+25}dx
integral of xsin^2(x)cos^2(x)	\int\:x\sin^{2}(x)\cos^{2}(x)dx
integral from 0 to 1 of (4x-4sqrt(x))	\int\:_{0}^{1}(4x-4\sqrt{x})dx
(dy)/(dx)+12y=8	\frac{dy}{dx}+12y=8
derivative of (sin(x^2)/(ln(2x+8)))	\frac{d}{dx}(\frac{\sin(x^{2})}{\ln(2x+8)})
integral of 1/(sqrt(x-1)+\sqrt[3]{x-1)}	\int\:\frac{1}{\sqrt{x-1}+\sqrt[3]{x-1}}dx
derivative of (1+sqrt(x))^3	derivative\:(1+\sqrt{x})^{3}
derivative of sec(pi/2)	\frac{d}{dx}(\sec(\frac{π}{2}))
(\partial)/(\partial x)(e^{-y}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-y}\cos(πx))
integral of (4t+9)^{2.1}	\int\:(4t+9)^{2.1}dt
derivative of f(x)= 1/(sqrt(x^5))	derivative\:f(x)=\frac{1}{\sqrt{x^{5}}}
derivative of A(e^{9x}+9e^{9x}x)	\frac{d}{dx}(A(e^{9x}+9e^{9x}x))
limit as x approaches 2 of 2sqrt(x-2)	\lim\:_{x\to\:2}(2\sqrt{x-2})
laplacetransform te^{2t}cos(5t)	laplacetransform\:te^{2t}\cos(5t)
derivative of (10+sec(θ))sin(θ)	derivative\:(10+\sec(θ))\sin(θ)
taylor 1/(1-x),8	taylor\:\frac{1}{1-x},8
derivative of x^2ln(x^5)	\frac{d}{dx}(x^{2}\ln(x^{5}))
f(x)=6e^x	f(x)=6e^{x}
integral of (5x^2-6)/(x^2-2x-8)	\int\:\frac{5x^{2}-6}{x^{2}-2x-8}dx
derivative of sin^2(3x+2)	\frac{d}{dx}(\sin^{2}(3x+2))
derivative of f(x)=cy^{-7}	derivative\:f(x)=cy^{-7}
tangent of f(x)=x^2+x,\at x=1,x=5	tangent\:f(x)=x^{2}+x,\at\:x=1,x=5
(dy}{dx}=\frac{(y^2))/x	\frac{dy}{dx}=\frac{(y^{2})}{x}
derivative of (1/2 ^{sqrt(sin^2(x))})	\frac{d}{dx}((\frac{1}{2})^{\sqrt{\sin^{2}(x)}})
derivative of 1/((2-x))	\frac{d}{dx}(\frac{1}{(2-x)})
integral of ((1-x)^2)/(x^2)	\int\:\frac{(1-x)^{2}}{x^{2}}dx
x^2+y^2+2xyy^'=0	x^{2}+y^{2}+2xyy^{\prime\:}=0
integral of (x+1)e^{-2x}	\int\:(x+1)e^{-2x}dx
derivative of f(x)=(x^2-2x-3)/x	derivative\:f(x)=\frac{x^{2}-2x-3}{x}
(\partial)/(\partial x)(3x^2-12y)	\frac{\partial\:}{\partial\:x}(3x^{2}-12y)
derivative of 4/(x-4)+(27)/(2x+2)	derivative\:\frac{4}{x-4}+\frac{27}{2x+2}
x^'-x=0	x^{\prime\:}-x=0
(\partial)/(\partial x)(ln(x^2+yx))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+yx))
area 10-7x,x^2-20,x=0	area\:10-7x,x^{2}-20,x=0
integral of (3x+2)\sqrt[3]{3x^2+4x}	\int\:(3x+2)\sqrt[3]{3x^{2}+4x}dx
derivative of ln(x^y)	\frac{d}{dx}(\ln(x^{y}))
integral of u^{-2}(2u^4+3u^2-2u^{-3})	\int\:u^{-2}(2u^{4}+3u^{2}-2u^{-3})du
derivative of (3x-4/(2x^2+5))	\frac{d}{dx}(\frac{3x-4}{2x^{2}+5})
derivative of x^2e^{-2x}	\frac{d}{dx}(x^{2}e^{-2x})
limit as x approaches 1/2 of \|2x+3\|	\lim\:_{x\to\:\frac{1}{2}}(\left\|2x+3\right\|)
(\partial)/(\partial x)(x^6y^8+7x^8y)	\frac{\partial\:}{\partial\:x}(x^{6}y^{8}+7x^{8}y)
derivative of-y/x	derivative\:-\frac{y}{x}
(3x+6y)dx+(6x-8y3)dy=0	(3x+6y)dx+(6x-8y3)dy=0
limit as x approaches 0 of x^2cos(3/x)	\lim\:_{x\to\:0}(x^{2}\cos(\frac{3}{x}))
integral of x(3x^2+5)^3	\int\:x(3x^{2}+5)^{3}dx
integral of (5x+5)/(4x^2+17x+4)	\int\:\frac{5x+5}{4x^{2}+17x+4}dx
derivative of cos(xsin(y))	\frac{d}{dx}(\cos(x)\sin(y))
taylor 1/(x^2),4	taylor\:\frac{1}{x^{2}},4
y^'=y(xy^6+5)	y^{\prime\:}=y(xy^{6}+5)
integral from 1 to 9 of 2^{sqrt(x)}	\int\:_{1}^{9}2^{\sqrt{x}}dx
integral of 2/((x+2)^2)	\int\:\frac{2}{(x+2)^{2}}dx
derivative of 3x^4+4x^3	\frac{d}{dx}(3x^{4}+4x^{3})
(\partial)/(\partial x)(60-x^2y^3)	\frac{\partial\:}{\partial\:x}(60-x^{2}y^{3})
integral from-125 to 27 of 1/(x^{1/3)}	\int\:_{-125}^{27}\frac{1}{x^{\frac{1}{3}}}dx
derivative of (2x^7-5x^4+2)^{25}	derivative\:(2x^{7}-5x^{4}+2)^{25}
integral of 7^{-x}	\int\:7^{-x}dx
d/(dt)((4+t)/(te^t))	\frac{d}{dt}(\frac{4+t}{te^{t}})
integral of x(6x+5)^8	\int\:x(6x+5)^{8}dx
derivative of f(x)=2e^x+2ln(x)	derivative\:f(x)=2e^{x}+2\ln(x)
sum from n=1 to infinity of sin(1/(n^2))	\sum\:_{n=1}^{\infty\:}\sin(\frac{1}{n^{2}})
integral of-1/(sin(θ))	\int\:-\frac{1}{\sin(θ)}dθ
y^'+t^2y=t^2	y^{\prime\:}+t^{2}y=t^{2}
derivative of 9xe^{-1/(y^3})	\frac{d}{dx}(9xe^{-\frac{1}{y^{3}}})
integral of 1/(sqrt(6-x^2))	\int\:\frac{1}{\sqrt{6-x^{2}}}dx
derivative of 5/(7x^2)	\frac{d}{dx}(\frac{5}{7x^{2}})
derivative of 3x+sqrt(x)	derivative\:3x+\sqrt{x}
(\partial)/(\partial u)((u-v)/(u+v))	\frac{\partial\:}{\partial\:u}(\frac{u-v}{u+v})
integral from 0 to 2 of (8ti-t^3j+3t^5k)	\int\:_{0}^{2}(8ti-t^{3}j+3t^{5}k)dt
integral of (e^{1/(x^9)})/(x^{10)}	\int\:\frac{e^{\frac{1}{x^{9}}}}{x^{10}}dx
limit as x approaches 6 of ((x^5-7776))/(x-6)	\lim\:_{x\to\:6}(\frac{(x^{5}-7776)}{x-6})
integral of 8xsqrt(4x^2+5)	\int\:8x\sqrt{4x^{2}+5}dx
limit as x approaches 1 of x+8	\lim\:_{x\to\:1}(x+8)
xy^'+y= 1/(y^2)	xy^{\prime\:}+y=\frac{1}{y^{2}}
integral of x^{12}ln(x)	\int\:x^{12}\ln(x)dx
(d^2y)/(dt^2)+3(dy)/(dt)+2y=0	\frac{d^{2}y}{dt^{2}}+3\frac{dy}{dt}+2y=0
integral of (2+tan(x))^2	\int\:(2+\tan(x))^{2}dx
f(x)=4sec^2(x)	f(x)=4\sec^{2}(x)
derivative of f(x)=5xsqrt(1-x^3)	derivative\:f(x)=5x\sqrt{1-x^{3}}
derivative of (7x+8/(4x+8))	\frac{d}{dx}(\frac{7x+8}{4x+8})
integral of 1.8^{(0.045x)}-1	\int\:1.8^{(0.045x)}-1dx
integral of-x^2e^{-x}	\int\:-x^{2}e^{-x}dx
(1-x^2)y^{''}-2xy^'=1	(1-x^{2})y^{\prime\:\prime\:}-2xy^{\prime\:}=1
limit as x approaches 0 of 1-sqrt(1-x)	\lim\:_{x\to\:0}(1-\sqrt{1-x})
2xy^'+y=6x	2xy^{\prime\:}+y=6x
(dy)/(dx)=(y-1)(1-2y)	\frac{dy}{dx}=(y-1)(1-2y)
integral of (7ln(x))/(x^3)	\int\:\frac{7\ln(x)}{x^{3}}dx
maclaurin ln(2+x)	maclaurin\:\ln(2+x)
derivative of 5arctan(x+sqrt(1+x^2))	\frac{d}{dx}(5\arctan(x+\sqrt{1+x^{2}}))
(dy)/(dx)=0.0015y(1200-y)	\frac{dy}{dx}=0.0015y(1200-y)
integral of 1/(7-8x)	\int\:\frac{1}{7-8x}dx
(\partial)/(\partial x)(7x^2+e^{2y})	\frac{\partial\:}{\partial\:x}(7x^{2}+e^{2y})
1/2 y^{''}+2y=tan(2t)-1/2 e^t	\frac{1}{2}y^{\prime\:\prime\:}+2y=\tan(2t)-\frac{1}{2}e^{t}
(\partial ^2)/(\partial {K)(b)\partial b}(bL^3{K}(b)(b)^2)	\frac{\partial\:^{2}}{\partial\:{K}(b)\partial\:b}(bL^{3}{K}(b)(b)^{2})
derivative of cos^2(2pix)	derivative\:\cos^{2}(2πx)
maclaurin sin(2x^2)	maclaurin\:\sin(2x^{2})
parity x^{tan(x)}	parity\:x^{\tan(x)}
derivative of (x^5/5-1/2 x^{-2})	\frac{d}{dx}(\frac{x^{5}}{5}-\frac{1}{2}x^{-2})
derivative of 4/(x^2+4)	derivative\:\frac{4}{x^{2}+4}
integral of 9sin^3(xco)s^2x	\int\:9\sin^{3}(xco)s^{2}xdx
derivative of (2u^2)/((u^2+u)^3)	derivative\:\frac{2u^{2}}{(u^{2}+u)^{3}}

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