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Popular Calculus Problems

integral from-infinity to 0 of 1/(4-8x)	\int\:_{-\infty\:}^{0}\frac{1}{4-8x}dx
y^'= x/((1+2y)),y(-1)=0	y^{\prime\:}=\frac{x}{(1+2y)},y(-1)=0
derivative of cos(x-2sin(x))	\frac{d}{dx}(\cos(x)-2\sin(x))
limit as x approaches 5-of 2/(x-5)	\lim\:_{x\to\:5-}(\frac{2}{x-5})
derivative of x^2y^3+xe^{xy}	\frac{d}{dx}(x^{2}y^{3}+xe^{xy})
integral of (10x+0.5)	\int\:(10x+0.5)dx
d/(d{y)}({x}^{({z})/({y)}})	\frac{d}{d{y}}({x}^{\frac{{z}}{{y}}})
derivative of 65536cos(2x)	\frac{d}{dx}(65536\cos(2x))
integral of (16x+4)sqrt(8x^2+4x)	\int\:(16x+4)\sqrt{8x^{2}+4x}dx
derivative of (3x^2+5)e^{4x}	derivative\:(3x^{2}+5)e^{4x}
integral of e^{cos(9t)}sin(9t)	\int\:e^{\cos(9t)}\sin(9t)dt
integral of sqrt(6+x^2)	\int\:\sqrt{6+x^{2}}dx
limit as x approaches-1 of x+1	\lim\:_{x\to\:-1}(x+1)
derivative of (ln(3x)^2)	\frac{d}{dx}((\ln(3x))^{2})
derivative of f(x)=(2x+x^2)/((1+x)^2)	derivative\:f(x)=\frac{2x+x^{2}}{(1+x)^{2}}
(\partial}{\partial x}(\frac{{Y}(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{{Y}(x)}{x})
xy^'-4y=6x^4e^x	xy^{\prime\:}-4y=6x^{4}e^{x}
tangent of f(x)=(-4x)/(x^2+1),\at x=-1	tangent\:f(x)=\frac{-4x}{x^{2}+1},\at\:x=-1
integral from 0 to 1 of 2/(x^2+1)	\int\:_{0}^{1}\frac{2}{x^{2}+1}dx
d/(d{x)}({x}^4+{y}^4+{z}^4)	\frac{d}{d{x}}({x}^{4}+{y}^{4}+{z}^{4})
derivative of sin(7x^2)	\frac{d}{dx}(\sin(7x^{2}))
x(dy)/(dx)=7xe^x-y+9x^2	x\frac{dy}{dx}=7xe^{x}-y+9x^{2}
limit as x approaches 1 of 2/(x^2-7x+6)	\lim\:_{x\to\:1}(\frac{2}{x^{2}-7x+6})
integral of e^{-r^2}*r	\int\:e^{-r^{2}}\cdot\:rdr
integral from 0 to 1 of sin^3(pi/2 x)	\int\:_{0}^{1}\sin^{3}(\frac{π}{2}x)dx
limit as x approaches 0 of 3x^2+1	\lim\:_{x\to\:0}(3x^{2}+1)
integral from 0 to x of t(e^{2t^3}-1)	\int\:_{0}^{x}t(e^{2t^{3}}-1)dt
implicit (dy)/(dx),x^3-xy+y^2=7	implicit\:\frac{dy}{dx},x^{3}-xy+y^{2}=7
derivative of (x-1/x)	\frac{d}{dx}(\frac{x-1}{x})
limit as x approaches 0 of 9/x-9/(x^2-x)	\lim\:_{x\to\:0}(\frac{9}{x}-\frac{9}{x^{2}-x})
derivative of ln(x)cos(x)	derivative\:\ln(x)\cos(x)
tangent of f(x)=(1+4x)^{(3/2)},\at x=2	tangent\:f(x)=(1+4x)^{(\frac{3}{2})},\at\:x=2
tangent of 6x^2-4x	tangent\:6x^{2}-4x
integral of 1/(x^9)	\int\:\frac{1}{x^{9}}dx
inverse oflaplace 2/((s^2+40s+400))	inverselaplace\:\frac{2}{(s^{2}+40s+400)}
area 2x+5,x^2+2x+1,[-2,2]	area\:2x+5,x^{2}+2x+1,[-2,2]
integral of 4x^{1/3}+2x^{-2/3}+9	\int\:4x^{\frac{1}{3}}+2x^{-\frac{2}{3}}+9dx
area y=x^2-6,y=5x	area\:y=x^{2}-6,y=5x
derivative of sin(tan(sqrt(sin(x))))	\frac{d}{dx}(\sin(\tan(\sqrt{\sin(x)})))
tangent of y=sqrt(1-4x)	tangent\:y=\sqrt{1-4x}
integral of tan(3)(x)sec(7)(x)	\int\:\tan(3)(x)\sec(7)(x)dx
derivative of x/(1+(1.5574+5.43x^2^2))	\frac{d}{dx}(\frac{x}{1+(1.5574+5.43x^{2})^{2}})
integral of x^5e^{-3x}	\int\:x^{5}e^{-3x}dx
sum from n=1 to infinity of (n!)/(102^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{102^{n}}
f(x)=-(x^3+x-1)/2	f(x)=-\frac{x^{3}+x-1}{2}
derivative of y= 9/(8\sqrt[4]{x^3)}	derivative\:y=\frac{9}{8\sqrt[4]{x^{3}}}
limit as x approaches 0 of a^x	\lim\:_{x\to\:0}(a^{x})
derivative of x^5-7x+8	derivative\:x^{5}-7x+8
y^{''}-4y^'+3y=cos(4t)	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=\cos(4t)
derivative of y=sqrt(x/(x+3))	derivative\:y=\sqrt{\frac{x}{x+3}}
y^{''}-4y^'+4y=(3x+8)e^{2x}+8x^2	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=(3x+8)e^{2x}+8x^{2}
integral of yln(y)-1/(sqrt(9-y^2))	\int\:y\ln(y)-\frac{1}{\sqrt{9-y^{2}}}dy
(\partial)/(\partial x)(2x-10)	\frac{\partial\:}{\partial\:x}(2x-10)
integral of ksqrt(t)	\int\:k\sqrt{t}dt
integral of x^3ze^{xz}	\int\:x^{3}ze^{xz}dx
sum from n=0 to infinity of-6(-1/3)^{2n}	\sum\:_{n=0}^{\infty\:}-6(-\frac{1}{3})^{2n}
derivative of f(x)=2x^3ln(x)	derivative\:f(x)=2x^{3}\ln(x)
derivative of (2x^2-4^3)	\frac{d}{dx}((2x^{2}-4)^{3})
derivative of (1-t)(3+t^2)^{-1}	derivative\:(1-t)(3+t^{2})^{-1}
derivative of y=(sin(x))/x	derivative\:y=\frac{\sin(x)}{x}
derivative of (x+5)/(x-5)	derivative\:\frac{x+5}{x-5}
y^'=5x+y	y^{\prime\:}=5x+y
integral of xsqrt(9x^2+4)	\int\:x\sqrt{9x^{2}+4}dx
integral of x^2e^{17x}	\int\:x^{2}e^{17x}dx
inverse oflaplace 1/(s-5)e^{-s}	inverselaplace\:\frac{1}{s-5}e^{-s}
roots sqrt(ax^2+\|x\|^3)	roots\:\sqrt{ax^{2}+\left\|x\right\|^{3}}
y^'=(-1+x+y)/(1+x)	y^{\prime\:}=\frac{-1+x+y}{1+x}
derivative of (9-ln(x))/(ln(x)-1)	derivative\:\frac{9-\ln(x)}{\ln(x)-1}
integral from 0 to 1 of 1/(x^{1/3)}	\int\:_{0}^{1}\frac{1}{x^{\frac{1}{3}}}dx
area 2x^2,8x-2x^2	area\:2x^{2},8x-2x^{2}
(2x-1)dx+(5y+3)dy=0	(2x-1)dx+(5y+3)dy=0
integral of sqrt(1+(16)/(x^{2/3))}	\int\:\sqrt{1+\frac{16}{x^{\frac{2}{3}}}}dx
integral from 4 to 2 of x	\int\:_{4}^{2}xdx
integral of (-x)/(e^x)	\int\:\frac{-x}{e^{x}}dx
integral of (cos(3x))/(sin^4(3x))	\int\:\frac{\cos(3x)}{\sin^{4}(3x)}dx
tangent of f(x)=2x^2-18x+5,\at x=0	tangent\:f(x)=2x^{2}-18x+5,\at\:x=0
limit as x approaches infinity of (3x^2-x-2)/(5x^2-4x+1)	\lim\:_{x\to\:\infty\:}(\frac{3x^{2}-x-2}{5x^{2}-4x+1})
derivative of f(x)=(x^2)/(3+8x)	derivative\:f(x)=\frac{x^{2}}{3+8x}
((x^2)/2)^'	(\frac{x^{2}}{2})^{\prime\:}
integral from 0 to 4 of xsqrt(17-x^2)	\int\:_{0}^{4}x\sqrt{17-x^{2}}dx
integral from 0 to 1 of (x^4+6)/x	\int\:_{0}^{1}\frac{x^{4}+6}{x}dx
simplify tan^4(2x-1)^3	simplify\:\tan^{4}(2x-1)^{3}
integral of x/(x+1-sqrt(x+1))	\int\:\frac{x}{x+1-\sqrt{x+1}}dx
limit as x approaches 1+of 3/(ln(x))-2/(x-1)	\lim\:_{x\to\:1+}(\frac{3}{\ln(x)}-\frac{2}{x-1})
tangent of y= 4/x ,(5, 4/5)	tangent\:y=\frac{4}{x},(5,\frac{4}{5})
derivative of (ln(7x))^2	derivative\:(\ln(7x))^{2}
(\partial)/(\partial x)(2^{-x})	\frac{\partial\:}{\partial\:x}(2^{-x})
integral of 8/((t^2+1)^{3/2)}	\int\:\frac{8}{(t^{2}+1)^{\frac{3}{2}}}dt
integral from-2 to 1 of x^3	\int\:_{-2}^{1}x^{3}dx
derivative of 2/(t^2)	derivative\:\frac{2}{t^{2}}
area sin(x),cos(x),0, pi/2	area\:\sin(x),\cos(x),0,\frac{π}{2}
(x-1)y^'-2+3x+y=0	(x-1)y^{\prime\:}-2+3x+y=0
integral from 0 to 1 of 1/(e^x+e^{-x)}	\int\:_{0}^{1}\frac{1}{e^{x}+e^{-x}}dx
derivative of-3ln(3+4x^2+5x^3-9)	\frac{d}{dx}(-3\ln(3+4x^{2})+5x^{3}-9)
derivative of y=6	derivative\:y=6
t^2(dy)/(dt)-t=1+y+ty,y(1)=10	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=10
derivative of 6x^6	\frac{d}{dx}(6x^{6})
integral from-35 to 0 of 1/(sqrt(1-x))	\int\:_{-35}^{0}\frac{1}{\sqrt{1-x}}dx
integral of (14)/x	\int\:\frac{14}{x}dx
derivative of f(x)=x^2*(x^3+2)	derivative\:f(x)=x^{2}\cdot\:(x^{3}+2)

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