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Popular Calculus Problems

derivative of sin(3x)+cos(4x)	derivative\:\sin(3x)+\cos(4x)
integral from 0 to 1 of 1/(x^{0.5)}	\int\:_{0}^{1}\frac{1}{x^{0.5}}dx
(\partial)/(\partial x)((3x+1)y)	\frac{\partial\:}{\partial\:x}((3x+1)y)
integral of ((x^2+1))/((x-4)(x-3)^2)	\int\:\frac{(x^{2}+1)}{(x-4)(x-3)^{2}}dx
y^{''}-10y^'+34y=0,y(0)=-2,y^'(0)=-3	y^{\prime\:\prime\:}-10y^{\prime\:}+34y=0,y(0)=-2,y^{\prime\:}(0)=-3
area 3/x , 3/(x^2),6	area\:\frac{3}{x},\frac{3}{x^{2}},6
area y=5,y=x^2+1	area\:y=5,y=x^{2}+1
simplify (x-2)^2sqrt(-3x)	simplify\:(x-2)^{2}\sqrt{-3x}
integral from-2 to 0 of \sqrt[3]{x^2}	\int\:_{-2}^{0}\sqrt[3]{x^{2}}dx
derivative of x^2sqrt(3-x)	\frac{d}{dx}(x^{2}\sqrt{3-x})
integral of 1/(5+x^2)	\int\:\frac{1}{5+x^{2}}dx
integral of (ln(y))/(log_{10)(y)}	\int\:\frac{\ln(y)}{\log_{10}(y)}dy
tangent of f(x)=x^4-17x^2+16	tangent\:f(x)=x^{4}-17x^{2}+16
integral of pi((sin(x))/x)^2	\int\:π(\frac{\sin(x)}{x})^{2}dx
integral from-1 to 1 of (5x)/((x+4)^2)	\int\:_{-1}^{1}\frac{5x}{(x+4)^{2}}dx
area y=\|x-6\|,y= x/2	area\:y=\left\|x-6\right\|,y=\frac{x}{2}
sum from n=1 to infinity of (2n)/(5n-3)	\sum\:_{n=1}^{\infty\:}\frac{2n}{5n-3}
derivative of e^{sin(2x)}	derivative\:e^{\sin(2x)}
integral from 0 to 1 of 2(1-x)	\int\:_{0}^{1}2(1-x)dx
integral of (4x)/(sqrt(4x^2+1))	\int\:\frac{4x}{\sqrt{4x^{2}+1}}dx
derivative of (2x/((x^2-3)^2))	\frac{d}{dx}(\frac{2x}{(x^{2}-3)^{2}})
derivative of y=e^{-x}cos(2x)	derivative\:y=e^{-x}\cos(2x)
inverse oflaplace 1/(s^4+s^2)	inverselaplace\:\frac{1}{s^{4}+s^{2}}
integral of (x^2+2x)	\int\:(x^{2}+2x)dx
integral of-3tan(3y)	\int\:-3\tan(3y)dy
derivative of (x-y/(sin(x)-sin(y)))	\frac{d}{dx}(\frac{x-y}{\sin(x)-\sin(y)})
(\partial)/(\partial y)(x^2sin^2(yz))	\frac{\partial\:}{\partial\:y}(x^{2}\sin^{2}(yz))
integral of x^{n-1}	\int\:x^{n-1}dx
inverse oflaplace 1/(sqrt(s))	inverselaplace\:\frac{1}{\sqrt{s}}
integral of sec^2(θ)+6	\int\:\sec^{2}(θ)+6dθ
derivative of (x^2)/(1+x)	derivative\:\frac{x^{2}}{1+x}
d/(d{r)}(ln({r}))	\frac{d}{d{r}}(\ln({r}))
area y=\sqrt[3]{x},y= 1/x ,x=8	area\:y=\sqrt[3]{x},y=\frac{1}{x},x=8
derivative of 2(x-3)	\frac{d}{dx}(2(x-3))
tangent of f(x)=(x^2)/(x+5),\at x=3	tangent\:f(x)=\frac{x^{2}}{x+5},\at\:x=3
derivative of aq^2	derivative\:aq^{2}
area 2x-x^2,2x-4	area\:2x-x^{2},2x-4
derivative of sin(xcot(x))	\frac{d}{dx}(\sin(x)\cot(x))
limit as x approaches 0+of-(2+ln(x))/x	\lim\:_{x\to\:0+}(-\frac{2+\ln(x)}{x})
integral from 0 to 2 of pi(8-x^3)^2	\int\:_{0}^{2}π(8-x^{3})^{2}dx
limit as x approaches-2 of x^4	\lim\:_{x\to\:-2}(x^{4})
sum from n=1 to infinity of (2n+1)^{-6}	\sum\:_{n=1}^{\infty\:}(2n+1)^{-6}
derivative of 9cos(2/5 x)	derivative\:9\cos(\frac{2}{5}x)
integral of (3x)/((x^2-3)^3)	\int\:\frac{3x}{(x^{2}-3)^{3}}dx
derivative of (2x-5/(2x+5))	\frac{d}{dx}(\frac{2x-5}{2x+5})
derivative of-x^2+x/3-3	\frac{d}{dx}(-x^{2}+\frac{x}{3}-3)
integral of-5xe^{x^2}	\int\:-5xe^{x^{2}}dx
integral of cos(7x)cos(3x)	\int\:\cos(7x)\cos(3x)dx
integral of e^{-sx}x^2	\int\:e^{-sx}x^{2}dx
integral of 125x^2cos(5x)	\int\:125x^{2}\cos(5x)dx
(\partial)/(\partial u)(u^2v^3)	\frac{\partial\:}{\partial\:u}(u^{2}v^{3})
limit as x approaches 0 of x^2-8	\lim\:_{x\to\:0}(x^{2}-8)
integral of x^5sqrt(x^3+4)	\int\:x^{5}\sqrt{x^{3}+4}dx
integral of ((x+5))/(x^2+10x+26)	\int\:\frac{(x+5)}{x^{2}+10x+26}dx
integral of 1/(x^2sqrt(2x^2-32))	\int\:\frac{1}{x^{2}\sqrt{2x^{2}-32}}dx
integral of sin^4(2x)*cos(2x)	\int\:\sin^{4}(2x)\cdot\:\cos(2x)dx
derivative of y= 1/((1+c_{1)e^{-x})}	derivative\:y=\frac{1}{(1+c_{1}e^{-x})}
(\partial)/(\partial x)(e^{xt})	\frac{\partial\:}{\partial\:x}(e^{xt})
derivative of 1/(x^{1/3})	\frac{d}{dx}(\frac{1}{x^{\frac{1}{3}}})
integral of z^2sin(x)	\int\:z^{2}\sin(x)dx
y^{''''}+y=0	y^{\prime\:\prime\:\prime\:\prime\:}+y=0
(dy)/(dx)=(y^2)/(2x+3)	\frac{dy}{dx}=\frac{y^{2}}{2x+3}
integral of (x^3)/(4-x^4)	\int\:\frac{x^{3}}{4-x^{4}}dx
integral of (sec^2(x))/(3+tan^2(x))	\int\:\frac{\sec^{2}(x)}{3+\tan^{2}(x)}dx
y^{''}-4y^'+3y=t,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=t,y(0)=1,y^{\prime\:}(0)=0
integral from 0 to 1 of (x-8)/(x^2-5x+6)	\int\:_{0}^{1}\frac{x-8}{x^{2}-5x+6}dx
derivative of (x^2/(ln(x)))	\frac{d}{dx}(\frac{x^{2}}{\ln(x)})
derivative of x^{3/5}sqrt(x^3+2x-6)	\frac{d}{dx}(x^{\frac{3}{5}}\sqrt{x^{3}+2x-6})
derivative of 2x^2-9x+10	\frac{d}{dx}(2x^{2}-9x+10)
inverse oflaplace (2s-44)/(7s^2-14s+70)	inverselaplace\:\frac{2s-44}{7s^{2}-14s+70}
(dx)/(dy)=((y-x))/(y+x)	\frac{dx}{dy}=\frac{(y-x)}{y+x}
area y=2,y=x^2+1	area\:y=2,y=x^{2}+1
derivative of (log_{2}(x)^4)	\frac{d}{dx}((\log_{2}(x))^{4})
y^{''}+3y^'=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+3y^{\prime\:}=0,y(0)=1,y^{\prime\:}(0)=1
derivative of 3x^{3/2}	derivative\:3x^{\frac{3}{2}}
slope of (2,3),(7,-6)	slope\:(2,3),(7,-6)
integral of (\sqrt[3]{x}-1/x)^2	\int\:(\sqrt[3]{x}-\frac{1}{x})^{2}dx
tangent of f(x)= 1/(sqrt(x+1)),(0,1)	tangent\:f(x)=\frac{1}{\sqrt{x+1}},(0,1)
area y=6e^x,y=6e^{-x},x=1	area\:y=6e^{x},y=6e^{-x},x=1
integral of 1/(y^2-9)	\int\:\frac{1}{y^{2}-9}dy
derivative of y(θ)=pi^4cos(θ)	derivative\:y(θ)=π^{4}\cos(θ)
d/(dt)(sqrt(9+t))	\frac{d}{dt}(\sqrt{9+t})
derivative of x+sqrt(2)cos(x)	\frac{d}{dx}(x+\sqrt{2}\cos(x))
derivative of x^2-2x+8	derivative\:x^{2}-2x+8
integral of x^5sqrt(1+x^3)	\int\:x^{5}\sqrt{1+x^{3}}dx
tangent of x^2+4x-11=-2y^2-3y,(2,-1)	tangent\:x^{2}+4x-11=-2y^{2}-3y,(2,-1)
integral of (3-x)^{-1/2}	\int\:(3-x)^{-\frac{1}{2}}dx
derivative of x^2+x+4	\frac{d}{dx}(x^{2}+x+4)
(dh)/(dt)=4-16t^2,h(1)=0	\frac{dh}{dt}=4-16t^{2},h(1)=0
derivative of ln(x^2-16x)	\frac{d}{dx}(\ln(x^{2}-16x))
integral of (y^2-1)	\int\:(y^{2}-1)dy
area x^3-13x^2+40x,-x^3+13x^2-40x	area\:x^{3}-13x^{2}+40x,-x^{3}+13x^{2}-40x
y^'=13xy-16x	y^{\prime\:}=13xy-16x
integral of ((2x^3+x-1))/(x^3+x^2-4x-4)	\int\:\frac{(2x^{3}+x-1)}{x^{3}+x^{2}-4x-4}dx
limit as x approaches 2 of pi^2-2x+5	\lim\:_{x\to\:2}(π^{2}-2x+5)
derivative of x(2x+7)^{2/3}	derivative\:x(2x+7)^{\frac{2}{3}}
limit as t approaches 2 of sqrt(8+t^3)	\lim\:_{t\to\:2}(\sqrt{8+t^{3}})
area y=e^{-x}sin(x),y=-e^{-x}sin(x),0<= x<= pi	area\:y=e^{-x}\sin(x),y=-e^{-x}\sin(x),0\le\:x\le\:π
integral of (cos(7x))/(1+sin^2(7x))	\int\:\frac{\cos(7x)}{1+\sin^{2}(7x)}dx
(dy)/(dx)= y/(x^2+1)	\frac{dy}{dx}=\frac{y}{x^{2}+1}

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