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Popular Calculus Problems

integral of x^7(x^8-9)^4	\int\:x^{7}(x^{8}-9)^{4}dx
integral of sin^2(θ)cos^2(θ)	\int\:\sin^{2}(θ)\cos^{2}(θ)dθ
limit as x approaches 0 of 1/x-1/(e^x-1)	\lim\:_{x\to\:0}(\frac{1}{x}-\frac{1}{e^{x}-1})
derivative of (x+2e^{2x})	\frac{d}{dx}((x+2)e^{2x})
(\partial)/(\partial x)(xln(y)+y^2z+z^2)	\frac{\partial\:}{\partial\:x}(x\ln(y)+y^{2}z+z^{2})
derivative of f(x)=6x-3	derivative\:f(x)=6x-3
(dx)/(dy)=(2y+sec^2(y))/(2x)	\frac{dx}{dy}=\frac{2y+\sec^{2}(y)}{2x}
integral from 0 to 0.5 of 250x	\int\:_{0}^{0.5}250xdx
integral of x/(1+2x)	\int\:\frac{x}{1+2x}dx
derivative of-(x+3(x-9)^2)	\frac{d}{dx}(-(x+3)(x-9)^{2})
integral of x*e^{xy}	\int\:x\cdot\:e^{xy}dy
integral of 16xe^{4x}	\int\:16xe^{4x}dx
tangent of sqrt(x^2+16)	tangent\:\sqrt{x^{2}+16}
factor 3x^3-12x^2+15x	factor\:3x^{3}-12x^{2}+15x
laplacetransform f(t)=t^2	laplacetransform\:f(t)=t^{2}
integral of 8y^{-3}	\int\:8y^{-3}dy
tangent of f(x)= 8/(x^2+4),\at x=4	tangent\:f(x)=\frac{8}{x^{2}+4},\at\:x=4
(\partial)/(\partial y)(x^2+y^2-4y)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-4y)
integral of xarctan(16x)	\int\:x\arctan(16x)dx
(\partial)/(\partial y)(x+x/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(x+\frac{x}{x^{2}+y^{2}})
(dy)/(dx)=4e^{-3x}	\frac{dy}{dx}=4e^{-3x}
integral of e^x*sin(e^x)	\int\:e^{x}\cdot\:\sin(e^{x})dx
limit as x approaches 3-of-(3)^2+5(3)-5	\lim\:_{x\to\:3-}(-(3)^{2}+5(3)-5)
tangent of 8sqrt(x)-2	tangent\:8\sqrt{x}-2
integral from 0 to 1 of (3e^{-x}-e^{-2x})	\int\:_{0}^{1}(3e^{-x}-e^{-2x})dx
y^{''}+6y^'+9y=27+e^{-3x}	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=27+e^{-3x}
integral of e^{3ln(4x-5)}	\int\:e^{3\ln(4x-5)}dx
f(x)=sqrt(5-3x)	f(x)=\sqrt{5-3x}
y^'-1=y^2	y^{\prime\:}-1=y^{2}
inverse oflaplace 2/(s(s^2+2s+2))	inverselaplace\:\frac{2}{s(s^{2}+2s+2)}
integral of 1/(1+\frac{2z){L}}	\int\:\frac{1}{1+\frac{2z}{L}}dz
integral of 1/(sqrt(x^2+6x+25))	\int\:\frac{1}{\sqrt{x^{2}+6x+25}}dx
maclaurin 1/(x+1)	maclaurin\:\frac{1}{x+1}
integral of (\sqrt[3]{x^2}+1)	\int\:(\sqrt[3]{x^{2}}+1)dx
integral of sin^2((pix)/L)	\int\:\sin^{2}(\frac{πx}{L})dx
t^2y^{''}-3ty^'+4y=0	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}+4y=0
(\partial)/(\partial y)((x+y)^5+(x-y)^5)	\frac{\partial\:}{\partial\:y}((x+y)^{5}+(x-y)^{5})
tangent of f(x)=x^2+5,(-5,30)	tangent\:f(x)=x^{2}+5,(-5,30)
xy^{''}-2y^'+4=0	xy^{\prime\:\prime\:}-2y^{\prime\:}+4=0
slope of (-3.7)(-4.12)	slope\:(-3.7)(-4.12)
tangent of f(x)=x^3(3-x)^4,\at x=2	tangent\:f(x)=x^{3}(3-x)^{4},\at\:x=2
limit as x approaches 100 of 20+0.188x	\lim\:_{x\to\:100}(20+0.188x)
integral of ysqrt(6+12y-36y^2)	\int\:y\sqrt{6+12y-36y^{2}}dy
derivative of (-1+x^2^{-1})	\frac{d}{dx}((-1+x^{2})^{-1})
integral from 1 to 5 of 6xln(x)	\int\:_{1}^{5}6x\ln(x)dx
integral of cos(x+nx)	\int\:\cos(x+nx)dx
(dy)/(dt)=ysin(t)	\frac{dy}{dt}=y\sin(t)
integral of (5+u)/u	\int\:\frac{5+u}{u}du
derivative of \sqrt[3]{1+\sqrt[3]{1+\sqrt[3]{x}}}	\frac{d}{dx}(\sqrt[3]{1+\sqrt[3]{1+\sqrt[3]{x}}})
integral from-2 to 2 of 1/(x^2-1)	\int\:_{-2}^{2}\frac{1}{x^{2}-1}dx
integral of (18)/x	\int\:\frac{18}{x}dx
tangent of f(x)=x^2-2x,\at x=3	tangent\:f(x)=x^{2}-2x,\at\:x=3
(\partial)/(\partial y)(e^x+ye^{xy})	\frac{\partial\:}{\partial\:y}(e^{x}+ye^{xy})
(\partial)/(\partial x)(e^y+x+x^2+2)	\frac{\partial\:}{\partial\:x}(e^{y}+x+x^{2}+2)
(dy)/(-yln(y/k))=cdx	\frac{dy}{-y\ln(\frac{y}{k})}=cdx
(dy)/(dx)+3y=30	\frac{dy}{dx}+3y=30
y^{''}+9y=-6tan(3x)	y^{\prime\:\prime\:}+9y=-6\tan(3x)
derivative of (2(e^{3sqrt(x)}))	\frac{d}{dx}((2)(e^{3\sqrt{x}}))
integral from 0 to 1 of t^2cos(npit)	\int\:_{0}^{1}t^{2}\cos(nπt)dt
(dy)/(dx)=sin^2(x)	\frac{dy}{dx}=\sin^{2}(x)
integral from 1 to 2 of x/((x+1)^2)	\int\:_{1}^{2}\frac{x}{(x+1)^{2}}dx
derivative of 3/((x+2^2))	\frac{d}{dx}(\frac{3}{(x+2)^{2}})
y^'=e^{4x}-3x	y^{\prime\:}=e^{4x}-3x
derivative of 2cot(x/2)	\frac{d}{dx}(2\cot(\frac{x}{2}))
y^'=x^2-y	y^{\prime\:}=x^{2}-y
36y^{''}-y=xe^{x/6},y(0)=1,y^'(0)=0	36y^{\prime\:\prime\:}-y=xe^{\frac{x}{6}},y(0)=1,y^{\prime\:}(0)=0
f^'(x)=1	f^{\prime\:}(x)=1
integral of 64x	\int\:64xdx
tangent of 2x^3+8x^2-5x+9	tangent\:2x^{3}+8x^{2}-5x+9
area 8-2x,x^3-7x^2+12x,[1,4]	area\:8-2x,x^{3}-7x^{2}+12x,[1,4]
limit as h approaches 0 of sqrt(h)	\lim\:_{h\to\:0}(\sqrt{h})
integral from 1 to 3 of 9r^3ln(r)	\int\:_{1}^{3}9r^{3}\ln(r)dr
(sec^3(x))^'	(\sec^{3}(x))^{\prime\:}
integral of sin(-7x)	\int\:\sin(-7x)dx
integral from 0 to 2 of (x^3)/2	\int\:_{0}^{2}\frac{x^{3}}{2}dx
(\partial)/(\partial x)(sqrt(x)e^{xy})	\frac{\partial\:}{\partial\:x}(\sqrt{x}e^{xy})
y^'=(xy(4-y))/(1+x)	y^{\prime\:}=\frac{xy(4-y)}{1+x}
derivative of x^4-25x^2+144	\frac{d}{dx}(x^{4}-25x^{2}+144)
(\partial)/(\partial x)(x(x^2+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}(x(x^{2}+y^{2})^{\frac{1}{2}})
derivative of 1+e^x	derivative\:1+e^{x}
y^{''}+2y^'+y=8e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=8e^{-t}
(dy)/(dx)=-(2xy+y^2+1)/(x^2+2xy)	\frac{dy}{dx}=-\frac{2xy+y^{2}+1}{x^{2}+2xy}
sum from k=1 to infinity of (2^k)/(k!)	\sum\:_{k=1}^{\infty\:}\frac{2^{k}}{k!}
derivative of x^2e^y	\frac{d}{dx}(x^{2}e^{y})
derivative of sqrt(x)-4\sqrt[3]{x}	derivative\:\sqrt{x}-4\sqrt[3]{x}
integral of s4^s	\int\:s4^{s}ds
integral from 0 to pi/2 of (cos(x))^2	\int\:_{0}^{\frac{π}{2}}(\cos(x))^{2}dx
sum from n=1 to infinity of 4^{1/(2^n)}	\sum\:_{n=1}^{\infty\:}4^{\frac{1}{2^{n}}}
derivative of y=(2^x)^8	derivative\:y=(2^{x})^{8}
integral of (x^2+2)^42x	\int\:(x^{2}+2)^{4}2xdx
4y^{''}+4y^'+8y=0	4y^{\prime\:\prime\:}+4y^{\prime\:}+8y=0
limit as x approaches 0 of cos(9x)	\lim\:_{x\to\:0}(\cos(9x))
sum from n=1 to infinity of n2^{-n}	\sum\:_{n=1}^{\infty\:}n2^{-n}
integral of xye^{y^2x}	\int\:xye^{y^{2}x}dy
derivative of 3/(e^x+e^{-x)}	derivative\:\frac{3}{e^{x}+e^{-x}}
derivative of ke^x	\frac{d}{dx}(ke^{x})
xsin(y/x)(dy)/(dx)=ysin(y/x)+x	x\sin(\frac{y}{x})\frac{dy}{dx}=y\sin(\frac{y}{x})+x
integral of 1/(a^2+v^2)	\int\:\frac{1}{a^{2}+v^{2}}dv
limit as x approaches 4+of 2/(x-4)	\lim\:_{x\to\:4+}(\frac{2}{x-4})
integral from 1 to e^5 of x^2ln(x)	\int\:_{1}^{e^{5}}x^{2}\ln(x)dx

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