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Popular Calculus Problems

derivative of x^2+x-1	\frac{d}{dx}(x^{2}+x-1)
integral of (3-1/(x^4))	\int\:(3-\frac{1}{x^{4}})dx
derivative of cos(2xdx)	\frac{d}{dx}(\cos(2x)dx)
derivative of (x^2-2^2)	\frac{d}{dx}((x^{2}-2)^{2})
derivative of (11-x)/7+(sqrt(36+x^2))/3	derivative\:\frac{11-x}{7}+\frac{\sqrt{36+x^{2}}}{3}
integral from 0 to 9 of \|2x-9\|	\int\:_{0}^{9}\left\|2x-9\right\|dx
limit as x approaches 3-of (e^2)/(x-3)	\lim\:_{x\to\:3-}(\frac{e^{2}}{x-3})
integral of (x^2)/((1-x^3)^5)	\int\:\frac{x^{2}}{(1-x^{3})^{5}}dx
derivative of 1/(sqrt(x^2+3))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}+3}})
derivative of (\sqrt[3]{x}/(x^3+1))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x^{3}+1})
integral of (cos(x))/(8-sin(x))	\int\:\frac{\cos(x)}{8-\sin(x)}dx
integral of 7/(9+16r^2)	\int\:\frac{7}{9+16r^{2}}dr
(dy)/(dx)=4y+3e^{8x}(x+1),y(0)=0	\frac{dy}{dx}=4y+3e^{8x}(x+1),y(0)=0
limit as x approaches 3-of (x+5)/(x-3)	\lim\:_{x\to\:3-}(\frac{x+5}{x-3})
integral of sin^3(x)cos^{-4}(x)	\int\:\sin^{3}(x)\cos^{-4}(x)dx
(20y^2-xy)dx+x^2dy=0	(20y^{2}-xy)dx+x^{2}dy=0
derivative of (12x^2-24x+24)e^{-8x}	derivative\:(12x^{2}-24x+24)e^{-8x}
integral of 1/(t^2sqrt(64-t^2))	\int\:\frac{1}{t^{2}\sqrt{64-t^{2}}}dt
3y^{''}+4y^'=0	3y^{\prime\:\prime\:}+4y^{\prime\:}=0
integral from 1 to e of x^4ln(x)	\int\:_{1}^{e}x^{4}\ln(x)dx
integral from 0 to pi of 4sin(x)	\int\:_{0}^{π}4\sin(x)dx
(\partial)/(\partial y)(2xln(y))	\frac{\partial\:}{\partial\:y}(2x\ln(y))
limit as x approaches 0+of 2-3/(x^{1/3)}	\lim\:_{x\to\:0+}(2-\frac{3}{x^{\frac{1}{3}}})
integral of (9e^{9x})/(5+e^{9x)}	\int\:\frac{9e^{9x}}{5+e^{9x}}dx
(y^'-e^{-t}+6)/y =-6,y(0)=1	\frac{y^{\prime\:}-e^{-t}+6}{y}=-6,y(0)=1
(\partial)/(\partial x)(5sin(2x)cos(5y))	\frac{\partial\:}{\partial\:x}(5\sin(2x)\cos(5y))
integral from 0 to 3 of sqrt(3x+16)	\int\:_{0}^{3}\sqrt{3x+16}dx
derivative of y=ln\|sin(x)\|	derivative\:y=\ln\left\|\sin(x)\right\|
derivative of (x^{2-x}^5(x-3x^2))	\frac{d}{dx}((x^{2-x})^{5}(x-3x^{2}))
integral of (81)/(x^3-9x^2)	\int\:\frac{81}{x^{3}-9x^{2}}dx
tangent of (x^2+1)/(x^2+x+1)	tangent\:\frac{x^{2}+1}{x^{2}+x+1}
derivative of f(x)=sqrt(7+10x)	derivative\:f(x)=\sqrt{7+10x}
area y=sqrt(x)+1,y=(x^2)/4 ,x=0,x=1	area\:y=\sqrt{x}+1,y=\frac{x^{2}}{4},x=0,x=1
y^'=(x^2-3y^2)/(2xy)	y^{\prime\:}=\frac{x^{2}-3y^{2}}{2xy}
limit as x approaches 11 of sqrt(3)	\lim\:_{x\to\:11}(\sqrt{3})
derivative of 3x-4x^{5/6}	\frac{d}{dx}(3x-4x^{\frac{5}{6}})
integral of 3ln(x^2-1)	\int\:3\ln(x^{2}-1)dx
2(dy}{dx}+1/x y=\frac{x^2)/y	2\frac{dy}{dx}+\frac{1}{x}y=\frac{x^{2}}{y}
y^{''}+4y^'+13y=0,y(0)=-1,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}+13y=0,y(0)=-1,y^{\prime\:}(0)=1
integral of 1/((x-6)(x-2))	\int\:\frac{1}{(x-6)(x-2)}dx
tangent of f(x)=4sec(x),\at pi/3	tangent\:f(x)=4\sec(x),\at\:\frac{π}{3}
integral of (3x^2(2x^3-1))	\int\:(3x^{2}(2x^{3}-1))dx
y^{''}+2y^'+y=0,y(0)=-4,y^'(0)=-1	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(0)=-4,y^{\prime\:}(0)=-1
derivative of e^x-1	derivative\:e^{x}-1
integral from 1 to infinity of x^{-5/4}	\int\:_{1}^{\infty\:}x^{-\frac{5}{4}}dx
integral of 1/(sqrt(x)+x)	\int\:\frac{1}{\sqrt{x}+x}dx
(\partial)/(\partial x)((x^2-y^2)/(z^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-y^{2}}{z^{2}})
derivative of x^3-3/2 x^2	\frac{d}{dx}(x^{3}-\frac{3}{2}x^{2})
integral of (x^3-x+2)/(x-1)	\int\:\frac{x^{3}-x+2}{x-1}dx
laplacetransform e^{-2t}cos^2(t)	laplacetransform\:e^{-2t}\cos^{2}(t)
(\partial)/(\partial y)(24y^2-12x)	\frac{\partial\:}{\partial\:y}(24y^{2}-12x)
(\partial)/(\partial x)(7Y(x))	\frac{\partial\:}{\partial\:x}(7Y(x))
inverse oflaplace (-5)/(s(6(5s+1)))	inverselaplace\:\frac{-5}{s(6(5s+1))}
derivative of f(x)=(7x^6+4x^3)^4	derivative\:f(x)=(7x^{6}+4x^{3})^{4}
(\partial)/(\partial x)(2x-y^2)	\frac{\partial\:}{\partial\:x}(2x-y^{2})
limit as x approaches 1 of x^2-6x+2	\lim\:_{x\to\:1}(x^{2}-6x+2)
integral of ((e^{-x}))/x	\int\:\frac{(e^{-x})}{x}dx
integral of 1/((64+x^2)^{3/2)}	\int\:\frac{1}{(64+x^{2})^{\frac{3}{2}}}dx
integral from 0 to 1 of (x/(1+x^2))	\int\:_{0}^{1}(\frac{x}{1+x^{2}})dx
xy^'+y=55sqrt(x)	xy^{\prime\:}+y=55\sqrt{x}
integral of (5sin(2x))/(sin(x))	\int\:\frac{5\sin(2x)}{\sin(x)}dx
y=10^{nx}	y=10^{nx}
integral of (e^{-3x})/x	\int\:\frac{e^{-3x}}{x}dx
derivative of x^2 1/2	\frac{d}{dx}(x^{2}\frac{1}{2})
derivative of 3x^{2/3}	derivative\:3x^{\frac{2}{3}}
integral of (x^2+1)/(x-1)	\int\:\frac{x^{2}+1}{x-1}dx
derivative of xe^{-8x}	derivative\:xe^{-8x}
derivative of (6x^{0.5}-x^2^2)	\frac{d}{dx}((6x^{0.5}-x^{2})^{2})
integral from 1 to 3 of (x/(x^2+1))	\int\:_{1}^{3}(\frac{x}{x^{2}+1})dx
derivative of 2-log_{10}(a)	derivative\:2-\log_{10}(a)
integral of (12x^2)/(2x+1)	\int\:\frac{12x^{2}}{2x+1}dx
limit as x approaches 0 of (4x^2-2x)/x	\lim\:_{x\to\:0}(\frac{4x^{2}-2x}{x})
(\partial)/(\partial x)(ln(x^2+3y^2+8))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+3y^{2}+8))
integral of 1/((x-2)(x-4)(x+1))	\int\:\frac{1}{(x-2)(x-4)(x+1)}dx
derivative of ax^4-2ax^3+2bx^2*ln(x/2)	\frac{d}{dx}(ax^{4}-2ax^{3}+2bx^{2}\cdot\:\ln(\frac{x}{2}))
derivative of x+2	derivative\:x+2
area x=-y^2+4y,[1,4]	area\:x=-y^{2}+4y,[1,4]
limit as x approaches 0 of sin^2(pi/x)	\lim\:_{x\to\:0}(\sin^{2}(\frac{π}{x}))
(\partial)/(\partial x)((9x+2y)^{10})	\frac{\partial\:}{\partial\:x}((9x+2y)^{10})
f(x)=e^{2x}+1	f(x)=e^{2x}+1
derivative of asin(5x+bcos(5x))	\frac{d}{dx}(a\sin(5x)+b\cos(5x))
y^'=-y	y^{\prime\:}=-y
derivative of (x^6)/(5-x^5)	derivative\:\frac{x^{6}}{5-x^{5}}
integral of 1/(sqrt(25x^2-4))	\int\:\frac{1}{\sqrt{25x^{2}-4}}dx
(\partial)/(\partial y)(e^xsin(y)+3y)	\frac{\partial\:}{\partial\:y}(e^{x}\sin(y)+3y)
integral of 1/(x^2+3x-4)	\int\:\frac{1}{x^{2}+3x-4}dx
integral of (x^2+1)/(x^3)	\int\:\frac{x^{2}+1}{x^{3}}dx
limit as x approaches 0 of sqrt(4-x)	\lim\:_{x\to\:0}(\sqrt{4-x})
(\partial)/(\partial x)(ln(xy)+ln(yz)+5ln(xz))	\frac{\partial\:}{\partial\:x}(\ln(xy)+\ln(yz)+5\ln(xz))
d/(dy)(1/(x^2+y^2))	\frac{d}{dy}(\frac{1}{x^{2}+y^{2}})
area x^2-4,x+2	area\:x^{2}-4,x+2
limit as x approaches 0 of-xln(x)	\lim\:_{x\to\:0}(-x\ln(x))
integral of sin(2x)-cos(3x)	\int\:\sin(2x)-\cos(3x)dx
y^{''}+y=x^2	y^{\prime\:\prime\:}+y=x^{2}
area y^2=4x,y=2x-4	area\:y^{2}=4x,y=2x-4
derivative of 4sqrt(x^2+3x)	\frac{d}{dx}(4\sqrt{x^{2}+3x})
(dx)/(dt)= x/t	\frac{dx}{dt}=\frac{x}{t}
(\partial)/(\partial x)(1/(\|x-a\|))	\frac{\partial\:}{\partial\:x}(\frac{1}{\left\|x-a\right\|})
area x=y^2-6y,x=5y-y^2	area\:x=y^{2}-6y,x=5y-y^{2}
integral of (-1)/(y^2)	\int\:\frac{-1}{y^{2}}dy

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