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Popular Calculus Problems

(\partial)/(\partial z)(e^{z^2})	\frac{\partial\:}{\partial\:z}(e^{z^{2}})
integral of 7(cos(x)+sin(x))/(sin(2x))	\int\:7\frac{\cos(x)+\sin(x)}{\sin(2x)}dx
(\partial)/(\partial x)(x^{y^2})	\frac{\partial\:}{\partial\:x}(x^{y^{2}})
(\partial)/(\partial y)(3x^2y^2-2)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{2}-2)
sum from n=1 to infinity of 1/((2n+1)^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n+1)^{2}}
sum from n=1 to infinity of (4n+1)/(4^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{4n+1}{4^{n+1}}
derivative of e^{(-x^2})	\frac{d}{dx}(e^{(-x^{2})})
integral of sin^3(7/3)x	\int\:\sin^{3}(\frac{7}{3})xdx
integral of 5/(9-x^2)	\int\:\frac{5}{9-x^{2}}dx
y^{''}+25y=cos(5x)+sin(5x)	y^{\prime\:\prime\:}+25y=\cos(5x)+\sin(5x)
sum from n=1 to infinity of 7/(3^{n-1)}	\sum\:_{n=1}^{\infty\:}\frac{7}{3^{n-1}}
integral of 1/(x^2+49)	\int\:\frac{1}{x^{2}+49}dx
area x^3,3x^2-4	area\:x^{3},3x^{2}-4
x^3y^'+3x^2y= 1/x ,y(1)=3	x^{3}y^{\prime\:}+3x^{2}y=\frac{1}{x},y(1)=3
(\partial)/(\partial x)(xsin(y)sin(z))	\frac{\partial\:}{\partial\:x}(x\sin(y)\sin(z))
integral of (x^2+1)^{1/2}x	\int\:(x^{2}+1)^{\frac{1}{2}}xdx
integral of (-3x+4)e-x	\int\:(-3x+4)e-xdx
integral from 0 to pi/2 of 7cos^2(x)	\int\:_{0}^{\frac{π}{2}}7\cos^{2}(x)dx
area y=x^2,y=-x^2+18x	area\:y=x^{2},y=-x^{2}+18x
derivative of f(x)=cx^{-7}	derivative\:f(x)=cx^{-7}
integral from 0 to pi/2 of sin^3(x)	\int\:_{0}^{\frac{π}{2}}\sin^{3}(x)dx
integral of-4x^2-4x+48	\int\:-4x^{2}-4x+48dx
limit as x approaches 0+of ln(7/(x^3))	\lim\:_{x\to\:0+}(\ln(\frac{7}{x^{3}}))
integral of 1/x-x	\int\:\frac{1}{x}-xdx
tangent of y= 3/x ,(-2,-3/2)	tangent\:y=\frac{3}{x},(-2,-\frac{3}{2})
integral of x^{1/9}	\int\:x^{\frac{1}{9}}dx
integral of (x+1)sec(x^2+2x)tan(x^2+2x)	\int\:(x+1)\sec(x^{2}+2x)\tan(x^{2}+2x)dx
derivative of sin^3(5x)	derivative\:\sin^{3}(5x)
limit as y approaches-3 of 4y^2+4y+1	\lim\:_{y\to\:-3}(4y^{2}+4y+1)
tangent of y=(sqrt(2))^x,\at x=8	tangent\:y=(\sqrt{2})^{x},\at\:x=8
partialfraction (x^2)/(x^2+1)	partialfraction\:\frac{x^{2}}{x^{2}+1}
f^'x=(2x)(x^4-8x)+(x^2)(4x^3-8)	f^{\prime\:}x=(2x)(x^{4}-8x)+(x^{2})(4x^{3}-8)
derivative of y=(6t-3)/(5t+8)	derivative\:y=\frac{6t-3}{5t+8}
limit as x approaches pi/2 of sin(x/2)	\lim\:_{x\to\:\frac{π}{2}}(\sin(\frac{x}{2}))
sum from n=3 to infinity of (e/pi)^n	\sum\:_{n=3}^{\infty\:}(\frac{e}{π})^{n}
derivative of 1/(sqrt(x^2+1))	derivative\:\frac{1}{\sqrt{x^{2}+1}}
inverse oflaplace 1/((s^2+4)(s^2+1))	inverselaplace\:\frac{1}{(s^{2}+4)(s^{2}+1)}
limit as x approaches 4-of cx^2+9x	\lim\:_{x\to\:4-}(cx^{2}+9x)
integral of sqrt(1+(4x^2)/((1-x^2)^2))	\int\:\sqrt{1+\frac{4x^{2}}{(1-x^{2})^{2}}}dx
y^{''}+8y^'+16y=0,y(0)=3,y^'(0)=-7	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0,y(0)=3,y^{\prime\:}(0)=-7
(\partial)/(\partial y)(3.25yzcos(xyz))	\frac{\partial\:}{\partial\:y}(3.25yz\cos(xyz))
derivative of x^{1/3}(x^2-4)	\frac{d}{dx}(x^{\frac{1}{3}}(x^{2}-4))
laplacetransform 5+4e-2t	laplacetransform\:5+4e-2t
(\partial)/(\partial x)(x^3y+xy^2+xy+x)	\frac{\partial\:}{\partial\:x}(x^{3}y+xy^{2}+xy+x)
derivative of (-200ln(x/(40))/(x+20))	\frac{d}{dx}(\frac{-200\ln(\frac{x}{40})}{x+20})
integral from 0 to 15 of 2pix(15x-x^2)	\int\:_{0}^{15}2πx(15x-x^{2})dx
(\partial)/(\partial x)(ln((2xy)/(5z)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2xy}{5z}))
integral of-9/(x^{10)}	\int\:-\frac{9}{x^{10}}dx
(\partial)/(\partial x)(u)	\frac{\partial\:}{\partial\:x}(u)
derivative of 4pix	\frac{d}{dx}(4πx)
limit as x approaches-2 of 1/(2x)	\lim\:_{x\to\:-2}(\frac{1}{2x})
integral of sin(x)+12x	\int\:\sin(x)+12xdx
derivative of sqrt(16x^3)	\frac{d}{dx}(\sqrt{16x^{3}})
derivative of f(x)= 1/(x^2)+1/(x^3)	derivative\:f(x)=\frac{1}{x^{2}}+\frac{1}{x^{3}}
(dy)/(dx)=y-5	\frac{dy}{dx}=y-5
derivative of (log_{2}(x)/x)	\frac{d}{dx}(\frac{\log_{2}(x)}{x})
derivative of (x^2)/(x-4)	derivative\:\frac{x^{2}}{x-4}
tangent of y=x^2+3,(-2,7)	tangent\:y=x^{2}+3,(-2,7)
integral from 0 to pi/2 of 45cos^5(x)	\int\:_{0}^{\frac{π}{2}}45\cos^{5}(x)dx
derivative of f(x)=2x+4x^{-1}	derivative\:f(x)=2x+4x^{-1}
f(x)=4xe^x	f(x)=4xe^{x}
derivative of x^3sin^2(5x)	\frac{d}{dx}(x^{3}\sin^{2}(5x))
integral of ln(5x^2)	\int\:\ln(5x^{2})dx
integral from 1 to 2 of 3sqrt(4x^2-3)	\int\:_{1}^{2}3\sqrt{4x^{2}-3}dx
area f(x)=2x,1,3	area\:f(x)=2x,1,3
integral of (cos(x))/(sin^2(x)-81)	\int\:\frac{\cos(x)}{\sin^{2}(x)-81}dx
limit as x approaches 0+of e^{sqrt(x)}	\lim\:_{x\to\:0+}(e^{\sqrt{x}})
derivative of ln(cos(e^{x^2-sec(x})))	\frac{d}{dx}(\ln(\cos(e^{x^{2}-\sec(x)})))
integral of 4ln(\sqrt[3]{x})	\int\:4\ln(\sqrt[3]{x})dx
integral of (9e^{-1/x})/(x^2)	\int\:\frac{9e^{-\frac{1}{x}}}{x^{2}}dx
tangent of f(x)=sqrt(x^2+1),\at x=2	tangent\:f(x)=\sqrt{x^{2}+1},\at\:x=2
tangent of x^4-4x^2+10,\at x=1	tangent\:x^{4}-4x^{2}+10,\at\:x=1
y^'+xy=0	y^{\prime\:}+xy=0
limit as x approaches 0+of cot^2(x)	\lim\:_{x\to\:0+}(\cot^{2}(x))
derivative of x^4-9x+6	\frac{d}{dx}(x^{4}-9x+6)
derivative of atan(x)	\frac{d}{dx}(a\tan(x))
integral of (t^2)/(sqrt(a^4+t^2))	\int\:\frac{t^{2}}{\sqrt{a^{4}+t^{2}}}dt
integral of (5/(x^2))	\int\:(\frac{5}{x^{2}})dx
derivative of f(x)=(x^2-4)*(x+4)	derivative\:f(x)=(x^{2}-4)\cdot\:(x+4)
derivative of (5sqrt(x)/6)	\frac{d}{dx}(\frac{5\sqrt{x}}{6})
integral of 2^x+4sinh(x)	\int\:2^{x}+4\sinh(x)dx
derivative of f(x)= 2/(sqrt(6+8x))	derivative\:f(x)=\frac{2}{\sqrt{6+8x}}
(\partial)/(\partial u)(2u)	\frac{\partial\:}{\partial\:u}(2u)
integral from-2 to 2 of 16-4y^2	\int\:_{-2}^{2}16-4y^{2}dy
limit as x approaches 0+of ln(x)-1/x	\lim\:_{x\to\:0+}(\ln(x)-\frac{1}{x})
x^2(dy)/(dx)+y^2=0	x^{2}\frac{dy}{dx}+y^{2}=0
derivative of x^3+7x-1	\frac{d}{dx}(x^{3}+7x-1)
derivative of f(x)=x(x^2+6)	derivative\:f(x)=x(x^{2}+6)
integral of-2sin^3(x)cos^2(x)	\int\:-2\sin^{3}(x)\cos^{2}(x)dx
derivative of e^{x+sqrt(x^2+1)}	\frac{d}{dx}(e^{x+\sqrt{x^{2}+1}})
derivative of sqrt(x-8)	derivative\:\sqrt{x-8}
(dy)/(dx)+1/x y=8x^2	\frac{dy}{dx}+\frac{1}{x}y=8x^{2}
limit as x approaches-2-of 4/(x+2)	\lim\:_{x\to\:-2-}(\frac{4}{x+2})
limit as x approaches-9 of (x^2-2)/(9-x)	\lim\:_{x\to\:-9}(\frac{x^{2}-2}{9-x})
integral of 2/(sec(x))	\int\:\frac{2}{\sec(x)}dx
integral of e^{-2v}	\int\:e^{-2v}dv
integral of 5cos(x/5)	\int\:5\cos(\frac{x}{5})dx
integral of cos(x)sin^7(x)	\int\:\cos(x)\sin^{7}(x)dx
integral of (3x^2-4x+1)	\int\:(3x^{2}-4x+1)dx
d/(dy)(2kqy(y^2+d^2)^{-3/2})	\frac{d}{dy}(2kqy(y^{2}+d^{2})^{-\frac{3}{2}})

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