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Popular Calculus Problems

sum from n=0 to infinity of (7^n)/(11^n)	\sum\:_{n=0}^{\infty\:}\frac{7^{n}}{11^{n}}
integral from 0 to 1 of 1/(x^3)	\int\:_{0}^{1}\frac{1}{x^{3}}dx
derivative of e^{sqrt(2)}+sqrt(2)^x	derivative\:e^{\sqrt{2}}+\sqrt{2}^{x}
limit as x approaches 0+of x^{15x}	\lim\:_{x\to\:0+}(x^{15x})
sum from n=5 to infinity of (4/5)^{-n}	\sum\:_{n=5}^{\infty\:}(\frac{4}{5})^{-n}
laplacetransform 9t	laplacetransform\:9t
area f(x)=(x-1)^2+2,x=-1,x=2	area\:f(x)=(x-1)^{2}+2,x=-1,x=2
integral of (5x^2-12x-12)/(x^3-4x)	\int\:\frac{5x^{2}-12x-12}{x^{3}-4x}dx
integral of (2x^5-x^3-1)/(x^3-4x)	\int\:\frac{2x^{5}-x^{3}-1}{x^{3}-4x}dx
limit as x approaches 1+of (2x)/(x-1)	\lim\:_{x\to\:1+}(\frac{2x}{x-1})
integral from 0 to 2 of (2x^2+1)	\int\:_{0}^{2}(2x^{2}+1)dx
integral of e^{x+2}	\int\:e^{x+2}dx
(\partial)/(\partial m)(mx^b)	\frac{\partial\:}{\partial\:m}(mx^{b})
derivative of sqrt(x-x^2)	\frac{d}{dx}(\sqrt{x-x^{2}})
(\partial)/(\partial x)(e^{3x^2y}(1+x-2y))	\frac{\partial\:}{\partial\:x}(e^{3x^{2}y}(1+x-2y))
derivative of sqrt(9-4x)	\frac{d}{dx}(\sqrt{9-4x})
integral of pi(x+1)^2	\int\:π(x+1)^{2}dx
limit as (x,y) approaches (0,9) of x^3y	\lim\:_{(x,y)\to\:(0,9)}(x^{3}y)
(\partial)/(\partial x)(e^{x*cos(y)})	\frac{\partial\:}{\partial\:x}(e^{x\cdot\:\cos(y)})
laplacetransform-5(t-2)e^{t-2}	laplacetransform\:-5(t-2)e^{t-2}
integral of xsin(1-x^2)	\int\:x\sin(1-x^{2})dx
integral of (7arcsin(x))/(x^2)	\int\:\frac{7\arcsin(x)}{x^{2}}dx
(dy)/(dx)=5x(y-1)^{1/5}	\frac{dy}{dx}=5x(y-1)^{\frac{1}{5}}
slope of-2x^5+11x^3	slope\:-2x^{5}+11x^{3}
derivative of (3-x(2-x)(5-x))	\frac{d}{dx}((3-x)(2-x)(5-x))
integral of (3x-2)e^x	\int\:(3x-2)e^{x}dx
integral of (x+3)^3	\int\:(x+3)^{3}dx
integral of 2x(x^2+2)^2	\int\:2x(x^{2}+2)^{2}dx
integral of 3cos^2(x)	\int\:3\cos^{2}(x)dx
f(x)=xsin(x)+cos(x)	f(x)=x\sin(x)+\cos(x)
(\partial)/(\partial x)(sin(3x+yz))	\frac{\partial\:}{\partial\:x}(\sin(3x+yz))
integral from 3 to infinity of 8/(x^2-x)	\int\:_{3}^{\infty\:}\frac{8}{x^{2}-x}dx
inverse oflaplace F(s)= 6/(s^2+4)	inverselaplace\:F(s)=\frac{6}{s^{2}+4}
integral of-6sin(2x)+3cos(3x)	\int\:-6\sin(2x)+3\cos(3x)dx
(dy}{dx}=\frac{15x)/y	\frac{dy}{dx}=\frac{15x}{y}
derivative of \sqrt[4]{x}	derivative\:\sqrt[4]{x}
d/(dy)(e^{xe^y})	\frac{d}{dy}(e^{xe^{y}})
area sqrt(x),x-2,y=0	area\:\sqrt{x},x-2,y=0
limit as x approaches 0 of (sin(kx))/x	\lim\:_{x\to\:0}(\frac{\sin(kx)}{x})
integral of (3r)/(sqrt(1-r^2))	\int\:\frac{3r}{\sqrt{1-r^{2}}}dr
integral of cos^2(4x)	\int\:\cos^{2}(4x)dx
derivative of y=(x/(3.3)+(3.3)/x)(x^2+1)	derivative\:y=(\frac{x}{3.3}+\frac{3.3}{x})(x^{2}+1)
limit as x approaches+2 of 2+sqrt(3)	\lim\:_{x\to\:+2}(2+\sqrt{3})
integral of (1+20w)sqrt(w)	\int\:(1+20w)\sqrt{w}dw
integral of (x^2)/((16-x^2)^{3/2)}	\int\:\frac{x^{2}}{(16-x^{2})^{\frac{3}{2}}}dx
derivative of e^{3x}*3	\frac{d}{dx}(e^{3x}\cdot\:3)
integral of cos(6y)-cos(-6y)	\int\:\cos(6y)-\cos(-6y)dy
derivative of 1/(3x+6)	\frac{d}{dx}(\frac{1}{3x+6})
derivative of (1/(1-2x))^3	derivative\:(\frac{1}{1-2x})^{3}
integral of (x^3-1)/(x^3+x)	\int\:\frac{x^{3}-1}{x^{3}+x}dx
integral of 1/(sqrt(x-1)*(x^2))	\int\:\frac{1}{\sqrt{x-1}\cdot\:(x^{2})}dx
derivative of-x(2x-y^3)	\frac{d}{dx}(-x(2x-y^{3}))
integral of (4+x)	\int\:(4+x)dx
taylor e^{1/θ}	taylor\:e^{\frac{1}{θ}}
sum from n=0 to infinity of 3/(nsqrt(n))	\sum\:_{n=0}^{\infty\:}\frac{3}{n\sqrt{n}}
integral of (sin(2x))/(1+cos^2(2x))	\int\:\frac{\sin(2x)}{1+\cos^{2}(2x)}dx
y^'=y(2+y)t,y(0)=1	y^{\prime\:}=y(2+y)t,y(0)=1
derivative of 9(sin(x))^x	derivative\:9(\sin(x))^{x}
integral of (sqrt(x^2-25))/(x^4)	\int\:\frac{\sqrt{x^{2}-25}}{x^{4}}dx
derivative of 4sqrt(x)-x	\frac{d}{dx}(4\sqrt{x}-x)
maclaurin xsin(-2x)	maclaurin\:x\sin(-2x)
integral of 2x	\int\:2xdx
integral of 7tsin^2(t)	\int\:7t\sin^{2}(t)dt
(\partial)/(\partial y)(arctan(x/y))	\frac{\partial\:}{\partial\:y}(\arctan(\frac{x}{y}))
(\partial)/(\partial y)(5arctan(x/y))	\frac{\partial\:}{\partial\:y}(5\arctan(\frac{x}{y}))
(dy)/(dx)=8yx	\frac{dy}{dx}=8yx
y^'=5xsqrt(3y+11),y(0)=3	y^{\prime\:}=5x\sqrt{3y+11},y(0)=3
derivative of f(x)=ln(ln(3x))	derivative\:f(x)=\ln(\ln(3x))
integral of 1/3 x^{-2/3}	\int\:\frac{1}{3}x^{-\frac{2}{3}}dx
derivative of t^5	derivative\:t^{5}
tangent of-3x^3-3x^2-x+3	tangent\:-3x^{3}-3x^{2}-x+3
derivative of 1/(xln(x^9))	\frac{d}{dx}(\frac{1}{x\ln(x^{9})})
y^'= y/x+x/y	y^{\prime\:}=\frac{y}{x}+\frac{x}{y}
y^{''}+y^'=sin(20x)	y^{\prime\:\prime\:}+y^{\prime\:}=\sin(20x)
(dy)/(dx)= 1/10 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{10}\sqrt{y}\cos^{2}(\sqrt{y})
derivative of (x^2+32sqrt(x)/8)	\frac{d}{dx}(\frac{x^{2}+32\sqrt{x}}{8})
integral from 0 to 1 of 2pi(2-y)(2y^2)	\int\:_{0}^{1}2π(2-y)(2y^{2})dy
integral from 2 to 3 of 1/(x^2)	\int\:_{2}^{3}\frac{1}{x^{2}}dx
integral of e^{x/6+4}	\int\:e^{\frac{x}{6}+4}dx
derivative of-3x^6ln(x)	\frac{d}{dx}(-3x^{6}\ln(x))
(\partial)/(\partial v)(1/3 (v-2u))	\frac{\partial\:}{\partial\:v}(\frac{1}{3}(v-2u))
integral of (7-x)^{49}	\int\:(7-x)^{49}dx
integral of (x^2+2)^2	\int\:(x^{2}+2)^{2}dx
integral of (tan^2(x)+sec^2(x))/(tan(x))	\int\:\frac{\tan^{2}(x)+\sec^{2}(x)}{\tan(x)}dx
integral of (2x)/(x^4+1)	\int\:\frac{2x}{x^{4}+1}dx
derivative of f(x)=12sqrt(x^3)-1/x	derivative\:f(x)=12\sqrt{x^{3}}-\frac{1}{x}
derivative of x^2+2x+2	derivative\:x^{2}+2x+2
derivative of (126-0.5x)x-50x-31.75	derivative\:(126-0.5x)x-50x-31.75
1-(dv)/(dx)=cos(v)	1-\frac{dv}{dx}=\cos(v)
(d^2)/(dx^2)(sqrt(x^2+9))	\frac{d^{2}}{dx^{2}}(\sqrt{x^{2}+9})
tangent of f(x)=-x^2-x+3,\at x=-3	tangent\:f(x)=-x^{2}-x+3,\at\:x=-3
integral of x^2sqrt(8-x^2)	\int\:x^{2}\sqrt{8-x^{2}}dx
integral of cot^2(x)(1+tan^2(x))	\int\:\cot^{2}(x)(1+\tan^{2}(x))dx
laplacetransform 6t^4	laplacetransform\:6t^{4}
tangent of f(x)=4-x^2,\at x=-1	tangent\:f(x)=4-x^{2},\at\:x=-1
integral of 1/(10x^7)	\int\:\frac{1}{10x^{7}}dx
y'=y(3-y)	y\prime\:=y(3-y)
integral of (cos(y)sin(x))	\int\:(\cos(y)\sin(x))dy
integral of (9sec^2(x))/(tan(x))	\int\:\frac{9\sec^{2}(x)}{\tan(x)}dx
limit as x approaches 2 of sqrt(x)+x	\lim\:_{x\to\:2}(\sqrt{x}+x)

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