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Popular Calculus Problems

integral from 4 to 5 of x	\int\:_{4}^{5}xdx
integral of e^{-x}cos(wx)	\int\:e^{-x}\cos(wx)dx
(dy)/(dx)=x^8y^{-3}	\frac{dy}{dx}=x^{8}y^{-3}
sum from n=1 to infinity of (1/4)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{4})^{n-1}
tangent of f(x)= 3/(sqrt(x)),\at x= 1/16	tangent\:f(x)=\frac{3}{\sqrt{x}},\at\:x=\frac{1}{16}
integral of 2tan^3(2x)sec^5(2x)	\int\:2\tan^{3}(2x)\sec^{5}(2x)dx
derivative of (x^3/3-(x^2)/2-6x+5)	\frac{d}{dx}(\frac{x^{3}}{3}-\frac{x^{2}}{2}-6x+5)
f(x)=ln(sin(x^2+1))	f(x)=\ln(\sin(x^{2}+1))
derivative of x^3-x^2-x+1	\frac{d}{dx}(x^{3}-x^{2}-x+1)
integral of cos(x+pi/2)	\int\:\cos(x+\frac{π}{2})dx
tangent of y=-9/2 x^2+3x+3,(-1,-9/2)	tangent\:y=-\frac{9}{2}x^{2}+3x+3,(-1,-\frac{9}{2})
limit as x approaches 2 of x^2-2	\lim\:_{x\to\:2}(x^{2}-2)
tangent of f(x)=-4x^4+x^3	tangent\:f(x)=-4x^{4}+x^{3}
taylor (z(z+1))/(z^2)	taylor\:\frac{z(z+1)}{z^{2}}
limit as x approaches pi+of h(x)	\lim\:_{x\to\:π+}(h(x))
(\partial)/(\partial x)(4pi^2LT^{-2})	\frac{\partial\:}{\partial\:x}(4π^{2}LT^{-2})
derivative of (7x^6+8x^3^4)	\frac{d}{dx}((7x^{6}+8x^{3})^{4})
integral of x^4(x+1)^4(2x+1)	\int\:x^{4}(x+1)^{4}(2x+1)dx
y^'=x-y	y^{\prime\:}=x-y
slope of (2.9)(5.8)	slope\:(2.9)(5.8)
integral of 1/(1+4x)	\int\:\frac{1}{1+4x}dx
integral of sin^3(x)cos^4(x)	\int\:\sin^{3}(x)\cos^{4}(x)dx
derivative of (xsin(x)/(x^2-1))	\frac{d}{dx}(\frac{x\sin(x)}{x^{2}-1})
integral of p(p+4)^5	\int\:p(p+4)^{5}dp
derivative of (e^x/(5+e^x))	\frac{d}{dx}(\frac{e^{x}}{5+e^{x}})
(\partial)/(\partial y)(2x-5y+3)	\frac{\partial\:}{\partial\:y}(2x-5y+3)
integral of (1+e^xy+xe^xy)	\int\:(1+e^{x}y+xe^{x}y)dx
integral from 1 to infinity of xe^{-2x}	\int\:_{1}^{\infty\:}xe^{-2x}dx
derivative of ax^2e^{-4x}	\frac{d}{dx}(ax^{2}e^{-4x})
(3dy)/(dx)+12y=4	\frac{3dy}{dx}+12y=4
(\partial)/(\partial x)(7x^{2y})	\frac{\partial\:}{\partial\:x}(7x^{2y})
derivative of-24+20x-10x^3+x^5	\frac{d}{dx}(-24+20x-10x^{3}+x^{5})
d/(dt)(t^2sin(t))	\frac{d}{dt}(t^{2}\sin(t))
laplacetransform e^t-pi	laplacetransform\:e^{t}-π
integral of (csc(7θ))/(csc(7θ)-sin(7θ))	\int\:\frac{\csc(7θ)}{\csc(7θ)-\sin(7θ)}dθ
limit as x approaches 3 of 4x-5	\lim\:_{x\to\:3}(4x-5)
derivative of tan^2(nx)	\frac{d}{dx}(\tan^{2}(nx))
derivative of-4/5 sin(x)	derivative\:-\frac{4}{5}\sin(x)
area y=2x^2-8,y=-5+5x	area\:y=2x^{2}-8,y=-5+5x
d/(dt)(2e^{-t^2}t)	\frac{d}{dt}(2e^{-t^{2}}t)
limit as x approaches 1 of ln(x)-5x	\lim\:_{x\to\:1}(\ln(x)-5x)
derivative of f(b)=(4-a-b-c)z	derivative\:f(b)=(4-a-b-c)z
limit as x approaches+(-0) of e^{1/x}	\lim\:_{x\to\:+(-0)}(e^{\frac{1}{x}})
d/(dt)(5cos(t))	\frac{d}{dt}(5\cos(t))
integral from 0 to 1 of 1/(sqrt(x^2+16))	\int\:_{0}^{1}\frac{1}{\sqrt{x^{2}+16}}dx
y^{''}-5y^'-2y=0	y^{\prime\:\prime\:}-5y^{\prime\:}-2y=0
integral from-8 to 8 of (8-\|x\|)	\int\:_{-8}^{8}(8-\left\|x\right\|)dx
limit as h approaches 0 of (x+h)^2-x^2	\lim\:_{h\to\:0}((x+h)^{2}-x^{2})
integral of (x+1)/(x(x^2+1))	\int\:\frac{x+1}{x(x^{2}+1)}dx
limit as x approaches-6 of (6-\|x\|)/(6+x)	\lim\:_{x\to\:-6}(\frac{6-\left\|x\right\|}{6+x})
integral of (sec(x)+tan(x))^2	\int\:(\sec(x)+\tan(x))^{2}dx
(\partial)/(\partial y)(2x+ycos(xy))	\frac{\partial\:}{\partial\:y}(2x+y\cos(xy))
integral from 0 to 2 of sqrt(17)	\int\:_{0}^{2}\sqrt{17}dx
derivative of e^{z/(z-3)}	derivative\:e^{\frac{z}{z-3}}
(d^2y)/(dx^2)=sqrt(2x-3)	\frac{d^{2}y}{dx^{2}}=\sqrt{2x-3}
limit as x approaches 2-of (x+2)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{x+2}{x^{2}-4})
integral of cos(4x)(1-sin(4x))^2	\int\:\cos(4x)(1-\sin(4x))^{2}dx
integral from 0 to 1 of 4/(1+x^2)	\int\:_{0}^{1}\frac{4}{1+x^{2}}dx
derivative of e^{xy}y	\frac{d}{dx}(e^{xy}y)
integral of (x+3)sqrt(7-x)	\int\:(x+3)\sqrt{7-x}dx
limit as x approaches 0 of x^4sin(3/x)	\lim\:_{x\to\:0}(x^{4}\sin(\frac{3}{x}))
derivative of (2x^3+5^4)	\frac{d}{dx}((2x^{3}+5)^{4})
integral of (sin(x))/(cos^2(x)-3cos(x))	\int\:\frac{\sin(x)}{\cos^{2}(x)-3\cos(x)}dx
tangent of f(x)=sqrt(x^2-x+4),\at x=4	tangent\:f(x)=\sqrt{x^{2}-x+4},\at\:x=4
integral of (8t^4+5t^3-6t^2+7t-9)	\int\:(8t^{4}+5t^{3}-6t^{2}+7t-9)dt
inverse oflaplace ((s+3))/((s^2+s+3))	inverselaplace\:\frac{(s+3)}{(s^{2}+s+3)}
derivative of-e^{-x}sin(x+e^{-x}cos(x))	\frac{d}{dx}(-e^{-x}\sin(x)+e^{-x}\cos(x))
(\partial)/(\partial x)(yz^2cos(x))	\frac{\partial\:}{\partial\:x}(yz^{2}\cos(x))
integral from-8 to 8 of ((64-x^2))/2	\int\:_{-8}^{8}\frac{(64-x^{2})}{2}dx
integral of 3/(sqrt(x^5))	\int\:\frac{3}{\sqrt{x^{5}}}dx
(\partial)/(\partial x)(x^4y^2-x^3y)	\frac{\partial\:}{\partial\:x}(x^{4}\cdot\:y^{2}-x^{3}\cdot\:y)
derivative of f(x)=e^{2x+1}	derivative\:f(x)=e^{2x+1}
derivative of x^3+ax^2y+bxy^2+y^3	\frac{d}{dx}(x^{3}+ax^{2}y+bxy^{2}+y^{3})
integral of 3x+2cos(5x)	\int\:3x+2\cos(5x)dx
integral of e^{0.5t}	\int\:e^{0.5t}dt
limit as x approaches 2 of ((3x-6))/(1-sqrt(4x-7))	\lim\:_{x\to\:2}(\frac{(3x-6)}{1-\sqrt{4x-7}})
(\partial)/(\partial x)(y^3+x^2y-3y)	\frac{\partial\:}{\partial\:x}(y^{3}+x^{2}y-3y)
(\partial)/(\partial y)(x^2y^3)	\frac{\partial\:}{\partial\:y}(x^{2}y^{3})
integral of 1/((x+2)(x^2+1))	\int\:\frac{1}{(x+2)(x^{2}+1)}dx
tangent of f(x)=sqrt(x-2),\at x=3	tangent\:f(x)=\sqrt{x-2},\at\:x=3
taylor cos(2x)+sin(x)	taylor\:\cos(2x)+\sin(x)
y^{''}-6y^'+9y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0
derivative of \sqrt[3]{8x^4}+1/(x^2)	derivative\:\sqrt[3]{8x^{4}}+\frac{1}{x^{2}}
integral from 0 to L of x	\int\:_{0}^{L}xdx
y^'+4y=x^2	y^{\prime\:}+4y=x^{2}
integral from-21 to 0 of 1/(sqrt(4-x))	\int\:_{-21}^{0}\frac{1}{\sqrt{4-x}}dx
integral of 8cos(x)	\int\:8\cos(x)dx
integral from 0 to 2 of 10x^3sqrt(x^2+4)	\int\:_{0}^{2}10x^{3}\sqrt{x^{2}+4}dx
(d^2y)/(dx^2)+2(dy)/(dx)-3y=2x-17	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}-3y=2x-17
(\partial)/(\partial y)(xtan(y))	\frac{\partial\:}{\partial\:y}(x\tan(y))
derivative of y=-2x^2-x+6	derivative\:y=-2x^{2}-x+6
integral from 0 to a of xsin^2(pi/a x)	\int\:_{0}^{a}x\sin^{2}(\frac{π}{a}x)dx
(\partial)/(\partial x)(-2xy^2)	\frac{\partial\:}{\partial\:x}(-2xy^{2})
(dx)/(dt)=x(1-x)	\frac{dx}{dt}=x(1-x)
integral of 6ln(x^2-1)	\int\:6\ln(x^{2}-1)dx
d/(dt)(ln(t))	\frac{d}{dt}(\ln(t))
(\partial)/(\partial x)(e^{-jwn})	\frac{\partial\:}{\partial\:x}(e^{-jwn})
(dy)/(dx)=((x-y))/((x+2y)),y(0)=1	\frac{dy}{dx}=\frac{(x-y)}{(x+2y)},y(0)=1
integral of (1/(sqrt(1+x+y)))	\int\:(\frac{1}{\sqrt{1+x+y}})dx
y^{''}+2y^'+18y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+18y=0,y(0)=1,y^{\prime\:}(0)=0

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