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Popular Calculus Problems

integral from 1 to 2 of (-y^3+2y^2+5y-6)	\int\:_{1}^{2}(-y^{3}+2y^{2}+5y-6)dy
integral from-3 to 3 of \|2x-1\|	\int\:_{-3}^{3}\left\|2x-1\right\|dx
derivative of 11+1/5 sin(11pit)	derivative\:11+\frac{1}{5}\sin(11πt)
integral of 3x^2sqrt(x^3+1)	\int\:3x^{2}\sqrt{x^{3}+1}dx
integral of (sin(x)-8cos(x))	\int\:(\sin(x)-8\cos(x))dx
integral from 0 to 1 of 4x^3e^{x^4}	\int\:_{0}^{1}4x^{3}e^{x^{4}}dx
xsqrt(1-y^2)dx+ysqrt(1+x^2)dy=0	x\sqrt{1-y^{2}}dx+y\sqrt{1+x^{2}}dy=0
integral from 0 to 1 of 1/(x^2-3)	\int\:_{0}^{1}\frac{1}{x^{2}-3}dx
integral of (9x^2+x+48)/((x+3)(x^2+9))	\int\:\frac{9x^{2}+x+48}{(x+3)(x^{2}+9)}dx
(\partial)/(\partial y)(xye^{sin(pixy)})	\frac{\partial\:}{\partial\:y}(xye^{\sin(πxy)})
area y=2,y=sec(x)	area\:y=2,y=\sec(x)
d/(dt)(sin^2(pit))	\frac{d}{dt}(\sin^{2}(πt))
d/(d{x)}(1/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{x}}(\frac{1}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
(\partial)/(\partial x)(xe^{x^2y})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}y})
derivative of (-40)/(x^7)	derivative\:\frac{-40}{x^{7}}
limit as x approaches 1+of x^{1/((1-x))}	\lim\:_{x\to\:1+}(x^{\frac{1}{(1-x)}})
limit as x approaches-infinity of x^2e^x	\lim\:_{x\to\:-\infty\:}(x^{2}e^{x})
derivative of f(x)=-9x^2+1640x-37000	derivative\:f(x)=-9x^{2}+1640x-37000
derivative of-1/(x+1)	\frac{d}{dx}(-\frac{1}{x+1})
d/(ds)(sL({y}(s)))	\frac{d}{ds}(sL({y}(s)))
integral of 1/(2x^2-12x+26)	\int\:\frac{1}{2x^{2}-12x+26}dx
integral of (1+arctan(x))/(1+x^2)	\int\:\frac{1+\arctan(x)}{1+x^{2}}dx
(\partial)/(\partial y)(1/2 (x-y)^2)	\frac{\partial\:}{\partial\:y}(\frac{1}{2}(x-y)^{2})
limit as x approaches 2 of x^2-4x+2	\lim\:_{x\to\:2}(x^{2}-4x+2)
inverse oflaplace 1/(2s^2+s)	inverselaplace\:\frac{1}{2s^{2}+s}
integral of 1/(x^1)	\int\:\frac{1}{x^{1}}dx
integral of (sin(1+sqrt(x)))/(sqrt(x))	\int\:\frac{\sin(1+\sqrt{x})}{\sqrt{x}}dx
integral from x to 5 of sin(t^3)	\int\:_{x}^{5}\sin(t^{3})dt
integral of tan^4(9x)	\int\:\tan^{4}(9x)dx
derivative of f(x)= 2/x-1/(x^2)	derivative\:f(x)=\frac{2}{x}-\frac{1}{x^{2}}
integral of (\sqrt[3]{x}+1/(sqrt(x)))	\int\:(\sqrt[3]{x}+\frac{1}{\sqrt{x}})dx
tangent of f(x)= x/(1+x^2),(2,0.4)	tangent\:f(x)=\frac{x}{1+x^{2}},(2,0.4)
integral from 0 to 2 of (x+2)-x^2	\int\:_{0}^{2}(x+2)-x^{2}dx
derivative of (1-sin(x)^{-1/2})	\frac{d}{dx}((1-\sin(x))^{-\frac{1}{2}})
derivative of ln(x/3 (x-3))	\frac{d}{dx}(\ln(\frac{x}{3})(x-3))
integral of (361)/(x^3-19x^2)	\int\:\frac{361}{x^{3}-19x^{2}}dx
derivative of-6sin(x)	\frac{d}{dx}(-6\sin(x))
derivative of 1/20 e^x+x^6-x^e+e	\frac{d}{dx}(\frac{1}{20}e^{x}+x^{6}-x^{e}+e)
(\partial)/(\partial x)(sin^9(x))	\frac{\partial\:}{\partial\:x}(\sin^{9}(x))
(\partial)/(\partial y)(y*cos(y-2x))	\frac{\partial\:}{\partial\:y}(y\cdot\:\cos(y-2x))
derivative of f(x)=x^2-x+1	derivative\:f(x)=x^{2}-x+1
limit as x approaches 0 of x^3	\lim\:_{x\to\:0}(x^{3})
derivative of (3x^2+3x-1^4)	\frac{d}{dx}((3x^{2}+3x-1)^{4})
8y^{''}-2y^'-y=4+5sin(2t)	8y^{\prime\:\prime\:}-2y^{\prime\:}-y=4+5\sin(2t)
area y=x^2-3x,y=2x+6	area\:y=x^{2}-3x,y=2x+6
derivative of f(x)=(2x)/(e^x)	derivative\:f(x)=\frac{2x}{e^{x}}
sum from n=1 to infinity of n!*x^n	\sum\:_{n=1}^{\infty\:}n!\cdot\:x^{n}
derivative of (x+a*e^{2x}+b)	\frac{d}{dx}((x+a)\cdot\:e^{2x}+b)
f(x)=4sin^2(x)	f(x)=4\sin^{2}(x)
integral of-x^2	\int\:-x^{2}dx
integral from 0 to 2 of xsqrt(4x^2+9)	\int\:_{0}^{2}x\sqrt{4x^{2}+9}dx
(e^{-(x^2)/2})^'	(e^{-\frac{x^{2}}{2}})^{\prime\:}
integral of 7/(sqrt(1-x^2))	\int\:\frac{7}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(35x^6y^4-24x^5y^3)	\frac{\partial\:}{\partial\:x}(35x^{6}y^{4}-24x^{5}y^{3})
(dy)/(dt)-3/t y=2t^3e^{2t}	\frac{dy}{dt}-\frac{3}{t}y=2t^{3}e^{2t}
derivative of x^3+2x^2-4x+2	\frac{d}{dx}(x^{3}+2x^{2}-4x+2)
sum from k=1 to infinity}e^{-sqrt(k of)	\sum\:_{k=1}^{\infty\:}e^{-\sqrt{k}}
limit as x approaches infinity of e^x-x	\lim\:_{x\to\:\infty\:}(e^{x}-x)
3v+(dv)/(dx)=0	3v+\frac{dv}{dx}=0
integral of (4+x^8)^58x^7	\int\:(4+x^{8})^{5}8x^{7}dx
integral of (sec^2(θ)+7)	\int\:(\sec^{2}(θ)+7)dθ
integral from 0 to 2 of (3x^2+2x)	\int\:_{0}^{2}(3x^{2}+2x)dx
integral of-3cos^2(x)sin(x)	\int\:-3\cos^{2}(x)\sin(x)dx
tangent of f(x)=3x^3+6x^2+19	tangent\:f(x)=3x^{3}+6x^{2}+19
(x+y)^2dx+(2xy+x^2-2)dy=0	(x+y)^{2}dx+(2xy+x^{2}-2)dy=0
integral of 2/(x^2+5x+6)	\int\:\frac{2}{x^{2}+5x+6}dx
limit as x approaches 0 of ((tan(ax)))/x	\lim\:_{x\to\:0}(\frac{(\tan(ax))}{x})
integral of cos(5x)sec^2(5x)	\int\:\cos(5x)\sec^{2}(5x)dx
derivative of (3x^2+9)(x^2-1x)	derivative\:(3x^{2}+9)(x^{2}-1x)
(2xy-9x^2)+(2y+x^2+1)(dy)/(dx)=0	(2xy-9x^{2})+(2y+x^{2}+1)\frac{dy}{dx}=0
slope of f(x)=-8x^2+8	slope\:f(x)=-8x^{2}+8
derivative of 3/5 x^{5/3}-3/4 x^{1/3}+5	derivative\:\frac{3}{5}x^{\frac{5}{3}}-\frac{3}{4}x^{\frac{1}{3}}+5
area y=x-1,y=0,x=9	area\:y=x-1,y=0,x=9
tangent of y=6x^2-x^3	tangent\:y=6x^{2}-x^{3}
derivative of f(x)=x^e	derivative\:f(x)=x^{e}
integral from-infinity to 0 of 1/(6-9x)	\int\:_{-\infty\:}^{0}\frac{1}{6-9x}dx
y^'-3y=7e^{3x},y(0)=0	y^{\prime\:}-3y=7e^{3x},y(0)=0
limit as x approaches a of b(ax-a^2+1)	\lim\:_{x\to\:a}(b(ax-a^{2}+1))
integral of 6e^x	\int\:6e^{x}dx
integral of sin^3(x)sqrt(cos(x))	\int\:\sin^{3}(x)\sqrt{\cos(x)}dx
integral of 15cos^3(2x)sin^5(2x)	\int\:15\cos^{3}(2x)\sin^{5}(2x)dx
derivative of x-2sin(x)	derivative\:x-2\sin(x)
derivative of \sqrt[3]{x}-1	\frac{d}{dx}(\sqrt[3]{x}-1)
derivative of 4x^2*2^{(3x+1})	\frac{d}{dx}(4x^{2}\cdot\:2^{(3x+1)})
((x+30)\sqrt[3]{2-x})^'	((x+30)\sqrt[3]{2-x})^{\prime\:}
(\partial)/(\partial x)((x^2+y^2)e^{y^2-x^2})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})e^{y^{2}-x^{2}})
integral of 2-x	\int\:2-xdx
limit as x approaches 3+of 4	\lim\:_{x\to\:3+}(4)
integral of 3/(\sqrt[5]{x^3)}	\int\:\frac{3}{\sqrt[5]{x^{3}}}dx
derivative of (3x^2-2x^2)	\frac{d}{dx}((3x^{2}-2x)^{2})
x^2(dy)/(dx)+y=0	x^{2}\frac{dy}{dx}+y=0
derivative of sin^2(6x)	\frac{d}{dx}(\sin^{2}(6x))
derivative of 1+sqrt(x-1)	\frac{d}{dx}(1+\sqrt{x-1})
(x^3-25x^2)^'	(x^{3}-25x^{2})^{\prime\:}
integral of arctan((2x)/(1-x^2))	\int\:\arctan(\frac{2x}{1-x^{2}})dx
(\partial)/(\partial x)(1+3x+2y^2)	\frac{\partial\:}{\partial\:x}(1+3x+2y^{2})
(\partial)/(\partial y)(y/(7x))	\frac{\partial\:}{\partial\:y}(\frac{y}{7x})
derivative of (4e^x/(cos(x)))	\frac{d}{dx}(\frac{4e^{x}}{\cos(x)})
integral from 1 to 4 of (sqrt(x))	\int\:_{1}^{4}(\sqrt{x})dx
(dy)/(dx)-y/x =6xe^x	\frac{dy}{dx}-\frac{y}{x}=6xe^{x}

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