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Popular Calculus Problems

limit as x approaches 0 of e^{xln(x)}	\lim\:_{x\to\:0}(e^{x\ln(x)})
integral of 1/(x^4sqrt(x^2-5))	\int\:\frac{1}{x^{4}\sqrt{x^{2}-5}}dx
(\partial)/(\partial x)(cos(x+y+z))	\frac{\partial\:}{\partial\:x}(\cos(x+y+z))
sum from k=1 to infinity of 2/3 (1.5)^{k-1}	\sum\:_{k=1}^{\infty\:}\frac{2}{3}(1.5)^{k-1}
f(x)=cos(3x^2)	f(x)=\cos(3x^{2})
derivative of sqrt(x/(x+7))	derivative\:\sqrt{\frac{x}{x+7}}
y^'=(3x^2sqrt(16+y^2))/y	y^{\prime\:}=\frac{3x^{2}\sqrt{16+y^{2}}}{y}
d/(dt)(te^{3t})	\frac{d}{dt}(te^{3t})
derivative of e^{-3/x}	\frac{d}{dx}(e^{-\frac{3}{x}})
limit as x approaches 0 of x*cot(x)	\lim\:_{x\to\:0}(x\cdot\:\cot(x))
derivative of x^2*2^x	\frac{d}{dx}(x^{2}\cdot\:2^{x})
derivative of 2xe^x	derivative\:2xe^{x}
derivative of e^{x^2}-1	\frac{d}{dx}(e^{x^{2}}-1)
derivative of x*e^x-1	\frac{d}{dx}(x\cdot\:e^{x}-1)
(\partial)/(\partial x)(4e^{x^7y})	\frac{\partial\:}{\partial\:x}(4e^{x^{7}y})
integral of sqrt(x^2-4x+29)	\int\:\sqrt{x^{2}-4x+29}dx
derivative of (1+x^2ln(1+x))	\frac{d}{dx}((1+x)^{2}\ln(1+x))
y^{10}y^'=13cos(pix)	y^{10}y^{\prime\:}=13\cos(πx)
integral of 7-3(1+x^2)^{-1}	\int\:7-3(1+x^{2})^{-1}dx
6x^{''}+1960x=0,x(0)=-3,x^'(0)=0	6x^{\prime\:\prime\:}+1960x=0,x(0)=-3,x^{\prime\:}(0)=0
tangent of f(x)=(sqrt(3))^x,\at x=8	tangent\:f(x)=(\sqrt{3})^{x},\at\:x=8
limit as x approaches 2 of 2^{c*x}	\lim\:_{x\to\:2}(2^{c\cdot\:x})
derivative of (6x/(2x^{1/3)})	\frac{d}{dx}(\frac{6x}{2x^{\frac{1}{3}}})
y^{''}+y=sin(x)	y^{\prime\:\prime\:}+y=\sin(x)
integral from 0 to 1 of 40 1/(x^p)	\int\:_{0}^{1}40\frac{1}{x^{p}}dx
integral of (x+2)\sqrt[3]{x^2+4x+2}	\int\:(x+2)\sqrt[3]{x^{2}+4x+2}dx
integral of ((((x)+1)*(x-1)))/((x))	\int\:\frac{(((x)+1)\cdot\:(x-1))}{(x)}dx
tangent of f(x)=x^2+2,(-2,6)	tangent\:f(x)=x^{2}+2,(-2,6)
integral of 2^{x-1}	\int\:2^{x-1}dx
derivative of (2)(e^{3xsqrt(x)})	derivative\:(2)(e^{3x\sqrt{x}})
integral of (x+1)e^{8x^2+16x}	\int\:(x+1)e^{8x^{2}+16x}dx
(\partial)/(\partial x)(1/(2x+y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2x+y})
limit as x approaches 5 of (x-5)/(x^2-5)	\lim\:_{x\to\:5}(\frac{x-5}{x^{2}-5})
integral of (tan^4(x))/(cos^2(x))	\int\:\frac{\tan^{4}(x)}{\cos^{2}(x)}dx
(dy)/(dx)=ye^x,y(0)=2e	\frac{dy}{dx}=ye^{x},y(0)=2e
derivative of sin(yx)	\frac{d}{dx}(\sin(yx))
d/(dt)(1+t^2)	\frac{d}{dt}(1+t^{2})
integral from 0 to 1 of (1-x)	\int\:_{0}^{1}(1-x)dx
integral of (4x^2)/(\sqrt[3]{3+5x)}	\int\:\frac{4x^{2}}{\sqrt[3]{3+5x}}dx
derivative of 5x^2+4sin(x)	\frac{d}{dx}(5x^{2}+4\sin(x))
sum from n=0 to infinity of (n/(n+2))^n	\sum\:_{n=0}^{\infty\:}(\frac{n}{n+2})^{n}
11x-4ysqrt(x^2+1)(dy)/(dx)=0,y(0)=8	11x-4y\sqrt{x^{2}+1}\frac{dy}{dx}=0,y(0)=8
limit as x approaches 2 of 5/x	\lim\:_{x\to\:2}(\frac{5}{x})
integral from 0 to infinity of 4e^{-x}	\int\:_{0}^{\infty\:}4e^{-x}dx
integral of (x/(2x+1))	\int\:(\frac{x}{2x+1})dx
derivative of-5^{8x^2-1}	\frac{d}{dx}(-5^{8x^{2}-1})
integral of 10sin^4(xco)s^2x	\int\:10\sin^{4}(xco)s^{2}xdx
tangent of 3x-5x^2	tangent\:3x-5x^{2}
(\partial)/(\partial x)(e^{sqrt(\|xyz\|)})	\frac{\partial\:}{\partial\:x}(e^{\sqrt{\left\|xyz\right\|}})
(\partial)/(\partial y)(y^2-2xy+6x)	\frac{\partial\:}{\partial\:y}(y^{2}-2xy+6x)
integral from 0 to 1 of x/(e^{x^2)}	\int\:_{0}^{1}\frac{x}{e^{x^{2}}}dx
(\partial)/(\partial y)((ax)/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{ax}{y^{2}})
integral of 1/(cos(8x))	\int\:\frac{1}{\cos(8x)}dx
integral from 0 to 2 of 6x(2-x)	\int\:_{0}^{2}6x(2-x)dx
derivative of (2x-3)e^{2-x}	derivative\:(2x-3)e^{2-x}
derivative of x^2+2y^2	\frac{d}{dx}(x^{2}+2y^{2})
derivative of \|x^3-3x^2+2\|	\frac{d}{dx}(\left\|x^{3}-3x^{2}+2\right\|)
tangent of y=x^2-2,(-3,7)	tangent\:y=x^{2}-2,(-3,7)
3xy^'=y^2-y-2	3xy^{\prime\:}=y^{2}-y-2
derivative of f(x)=ln(3x)	derivative\:f(x)=\ln(3x)
integral of 1/((4-x^2))	\int\:\frac{1}{(4-x^{2})}dx
integral of (1-x)^{1/2}	\int\:(1-x)^{\frac{1}{2}}dx
integral of 9x(9-x^{-4})	\int\:9x(9-x^{-4})dx
derivative of {u}(x(x)^3+4)	\frac{d}{dx}({u}(x)(x)^{3}+4)
limit as x approaches 3-of (x-3)/(x^2-9)	\lim\:_{x\to\:3-}(\frac{x-3}{x^{2}-9})
tangent of y=(x^3-25x)^{12},(5,0)	tangent\:y=(x^{3}-25x)^{12},(5,0)
integral of xsin(x	\int\:x\sin(d)xdx
limit as x approaches pi/4 of sec(x)	\lim\:_{x\to\:\frac{π}{4}}(\sec(x))
(d^2)/(dx^2)(sqrt(r)+\sqrt[8]{r})	\frac{d^{2}}{dx^{2}}(\sqrt{r}+\sqrt[8]{r})
inverse oflaplace 2/(3(s-3)^2+12)	inverselaplace\:\frac{2}{3(s-3)^{2}+12}
integral of x(x^2+1)^2	\int\:x(x^{2}+1)^{2}dx
derivative of 3^{sin(pix})	\frac{d}{dx}(3^{\sin(πx)})
derivative of (ln(x)^7)	\frac{d}{dx}((\ln(x))^{7})
derivative of y=sqrt(13-x^9)	derivative\:y=\sqrt{13-x^{9}}
(\partial)/(\partial x)(6x^2e^y-7xy^3)	\frac{\partial\:}{\partial\:x}(6x^{2}e^{y}-7xy^{3})
integral of ((1+cot^2(z))cot(z))/(csc(z))	\int\:\frac{(1+\cot^{2}(z))\cot(z)}{\csc(z)}dz
integral of ze^y	\int\:ze^{y}dy
(dy)/(dt)=1+t+y+ty	\frac{dy}{dt}=1+t+y+ty
derivative of x^2+2x-8	\frac{d}{dx}(x^{2}+2x-8)
(\partial)/(\partial x)(e^{-x}tan(y))	\frac{\partial\:}{\partial\:x}(e^{-x}\tan(y))
laplacetransform e^{-2t}sin(3pit)	laplacetransform\:e^{-2t}\sin(3πt)
(dy)/(dx)+2y=50	\frac{dy}{dx}+2y=50
d/(dt)(6sin^3(t))	\frac{d}{dt}(6\sin^{3}(t))
(d^2)/(dx^2)(5/(6t^4))	\frac{d^{2}}{dx^{2}}(\frac{5}{6t^{4}})
(dy)/(dx)=((x+y)^2)/(2x^2)	\frac{dy}{dx}=\frac{(x+y)^{2}}{2x^{2}}
derivative of x^2-4xy+y^2	\frac{d}{dx}(x^{2}-4xy+y^{2})
x^2y^'+xy=9	x^{2}y^{\prime\:}+xy=9
derivative of ln(x(x-1))	\frac{d}{dx}(\ln(x)(x-1))
implicit (dy)/(dx),5cos(8x)sin(5y)=8	implicit\:\frac{dy}{dx},5\cos(8x)\sin(5y)=8
y^{''}=12t-2	y^{\prime\:\prime\:}=12t-2
derivative of (6x^2+3x+7)/(sqrt(x))	derivative\:\frac{6x^{2}+3x+7}{\sqrt{x}}
y^'=0.0011y*(2900-y)	y^{\prime\:}=0.0011y\cdot\:(2900-y)
integral of 8e^{5x+e^{5x}}	\int\:8e^{5x+e^{5x}}dx
integral of cot^2(x)csc^6(x)	\int\:\cot^{2}(x)\csc^{6}(x)dx
derivative of (x^{2.3}+4)/(x^{3.5)+1}	derivative\:\frac{x^{2.3}+4}{x^{3.5}+1}
integral of wln(w)	\int\:w\ln(w)dw
y^'+3/(2x)y=0	y^{\prime\:}+\frac{3}{2x}y=0
integral from 1 to 5 of (4x-1)	\int\:_{1}^{5}(4x-1)dx
integral of ln(xy)	\int\:\ln(xy)dx
integral from-infinity to 10 of xe^{x/5}	\int\:_{-\infty\:}^{10}xe^{\frac{x}{5}}dx

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