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Popular Calculus Problems

integral of 1/((2-3x))	\int\:\frac{1}{(2-3x)}dx
integral of 7/(x^2)	\int\:\frac{7}{x^{2}}dx
integral of 20x^3	\int\:20x^{3}dx
(dQ)/(dt)=0.03(1-Q)^{2/3}	\frac{dQ}{dt}=0.03(1-Q)^{\frac{2}{3}}
sum from n=1 to infinity}(e^{npi of)/(pi^{ne)}	\sum\:_{n=1}^{\infty\:}\frac{e^{nπ}}{π^{ne}}
y^{''}-3y^'-54y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-54y=0
derivative of x^{8cos(x})	\frac{d}{dx}(x^{8\cos(x)})
integral of-x/(1-x)	\int\:-\frac{x}{1-x}dx
tangent of y=-x^3+9x^2-6x+9,(7,65)	tangent\:y=-x^{3}+9x^{2}-6x+9,(7,65)
y^'=(4x^3+1)/(2y-6)	y^{\prime\:}=\frac{4x^{3}+1}{2y-6}
d/(dt)((tsin(t))/(1+t))	\frac{d}{dt}(\frac{t\sin(t)}{1+t})
integral of 0.1x^2	\int\:0.1x^{2}dx
integral of 6/(x^2-x-2)	\int\:\frac{6}{x^{2}-x-2}dx
y^'(1-xy^{1985})=y^{1986}	y^{\prime\:}(1-xy^{1985})=y^{1986}
integral of (5x^3-3sqrt(x))/x	\int\:\frac{5x^{3}-3\sqrt{x}}{x}dx
integral from 2sqrt(2) to 4 of 1/(t^3sqrt(t^2-4))	\int\:_{2\sqrt{2}}^{4}\frac{1}{t^{3}\sqrt{t^{2}-4}}dt
y^'+ycos(x)=0	y^{\prime\:}+y\cos(x)=0
taylor sqrt(x+1)	taylor\:\sqrt{x+1}
integral from 1 to 2 of (x^2+8)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+8}{3x-x^{2}}dx
derivative of (x^2/(sqrt(x^2-1)))	\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{2}-1}})
derivative of (7+2x)/(5-8x)	derivative\:\frac{7+2x}{5-8x}
(\partial)/(\partial x)(1/(tan(xy)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\tan(xy)})
(dy)/(dx)=(x+y+2)^2	\frac{dy}{dx}=(x+y+2)^{2}
(\partial)/(\partial x)(e^{-2x}*cos(2y))	\frac{\partial\:}{\partial\:x}(e^{-2x}\cdot\:\cos(2y))
integral of (5x-3)/(x^2-1)	\int\:\frac{5x-3}{x^{2}-1}dx
tangent of y= 6/(sqrt(x))	tangent\:y=\frac{6}{\sqrt{x}}
integral of 7(sin(x))^4(cos(x))^2	\int\:7(\sin(x))^{4}(\cos(x))^{2}dx
x(dy)/(dx)=x^3+14x^3y	x\frac{dy}{dx}=x^{3}+14x^{3}y
derivative of (ln(x)^2)	\frac{d}{dx}((\ln(x))^{2})
integral of cxy+1/4	\int\:cxy+\frac{1}{4}
tangent of f(x)=(sqrt(x))/(4x-7),\at x=1	tangent\:f(x)=\frac{\sqrt{x}}{4x-7},\at\:x=1
tangent of-5x^2+x-2	tangent\:-5x^{2}+x-2
integral from 0 to 9 of 1/(81+x^2)	\int\:_{0}^{9}\frac{1}{81+x^{2}}dx
y^{''}+4y^'+5y=-20e^t,y(0)=-4,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-20e^{t},y(0)=-4,y^{\prime\:}(0)=1
integral from 1 to 4 of 6e^{sqrt(x)}	\int\:_{1}^{4}6e^{\sqrt{x}}dx
critical f(x,y)=(x)^2+(y)^4	critical\:f(x,y)=(x)^{2}+(y)^{4}
limit as x approaches 3+of 1/(\|x-3\|)	\lim\:_{x\to\:3+}(\frac{1}{\left\|x-3\right\|})
limit as y approaches 0 of (y^2)/(y^4)	\lim\:_{y\to\:0}(\frac{y^{2}}{y^{4}})
derivative of f(x)=e^x-x^7	derivative\:f(x)=e^{x}-x^{7}
limit as x approaches 1 of (x^2-9)/(x-3)	\lim\:_{x\to\:1}(\frac{x^{2}-9}{x-3})
area y^2=4x+4,y=4x-16	area\:y^{2}=4x+4,y=4x-16
limit as x approaches+0 of e^{4x+2}	\lim\:_{x\to\:+0}(e^{4x+2})
derivative of tan^n(x)	\frac{d}{dx}(\tan^{n}(x))
integral of e^{-x^6}(-6x^5)	\int\:e^{-x^{6}}(-6x^{5})dx
integral of (2x)/((x^2+4)^2)	\int\:\frac{2x}{(x^{2}+4)^{2}}dx
implicit (dy)/(dx),-x+y-x^3=y^3+4x^2	implicit\:\frac{dy}{dx},-x+y-x^{3}=y^{3}+4x^{2}
integral of ((x+1)^2)/(x^2)	\int\:\frac{(x+1)^{2}}{x^{2}}dx
integral of 1/(n(n+1))	\int\:\frac{1}{n(n+1)}
y^{''}-3y^'-18y=0	y^{\prime\:\prime\:}-3y^{\prime\:}-18y=0
area x^3-15x^2+50x,-x^3+15x^2-50x	area\:x^{3}-15x^{2}+50x,-x^{3}+15x^{2}-50x
sum from n=0 to infinity of 1/(2n+3)	\sum\:_{n=0}^{\infty\:}\frac{1}{2n+3}
-2y^'+6x^2=0	-2y^{\prime\:}+6x^{2}=0
integral of (-x^2+x+4)/(x(x-2)^2)	\int\:\frac{-x^{2}+x+4}{x(x-2)^{2}}dx
sum from n=1 to infinity of ln((n+1)/n)	\sum\:_{n=1}^{\infty\:}\ln(\frac{n+1}{n})
9y^{''}-y=(xex)/3	9y^{\prime\:\prime\:}-y=\frac{xex}{3}
integral of sin(x)x	\int\:\sin(x)xdx
integral from 3 to 8 of x^3ln(3x)	\int\:_{3}^{8}x^{3}\ln(3x)dx
y^{''}-8y^'+20y=200x^2-39xe^x	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=200x^{2}-39xe^{x}
integral from 0 to 8 of xe^{-x}	\int\:_{0}^{8}xe^{-x}dx
derivative of-x/(x^2+y^2)	\frac{d}{dx}(-\frac{x}{x^{2}+y^{2}})
integral of 1/(sqrt(2-3x^2))	\int\:\frac{1}{\sqrt{2-3x^{2}}}dx
limit as x approaches pi-of cot(x)	\lim\:_{x\to\:π-}(\cot(x))
derivative of 8e^{4x}	derivative\:8e^{4x}
slope of xy-5y^2=4	slope\:xy-5y^{2}=4
laplacetransform 4te^{3t}sin(2t)	laplacetransform\:4te^{3t}\sin(2t)
integral of sqrt(18-18sin(x))	\int\:\sqrt{18-18\sin(x)}dx
limit as x approaches infinity of 1/(x!)	\lim\:_{x\to\:\infty\:}(\frac{1}{x!})
derivative of-1/(x^{2/3)}	derivative\:-\frac{1}{x^{\frac{2}{3}}}
derivative of sinh^2(3x)	\frac{d}{dx}(\sinh^{2}(3x))
y^{''}+4y=0,y(0)=4,y^'(0)=1	y^{\prime\:\prime\:}+4y=0,y(0)=4,y^{\prime\:}(0)=1
integral of (cos(9x))	\int\:(\cos(9x))dx
derivative of 2xe^x+3sec(x)	\frac{d}{dx}(2xe^{x}+3\sec(x))
derivative of ln((ax^n))	\frac{d}{dx}(\ln((ax)^{n}))
(dy)/(dx)=y(1-y),y(0)=8	\frac{dy}{dx}=y(1-y),y(0)=8
limit as x approaches 4-of 3x-5	\lim\:_{x\to\:4-}(3x-5)
derivative of 4x^3-56x^2+196x	derivative\:4x^{3}-56x^{2}+196x
integral of 1/((sin(x)+cos(x))^2)	\int\:\frac{1}{(\sin(x)+\cos(x))^{2}}dx
integral of 2x^3e^{-2x}	\int\:2x^{3}e^{-2x}dx
limit as x approaches pi/4 of (cos(2x))/(sqrt(2)cos(x)-1)	\lim\:_{x\to\:\frac{π}{4}}(\frac{\cos(2x)}{\sqrt{2}\cos(x)-1})
cos^2(x)sin(x)dy+(ycos^3(x)-1)dx=0	\cos^{2}(x)\sin(x)dy+(y\cos^{3}(x)-1)dx=0
x^2(dy)/(dx)+2xy=5y^3	x^{2}\frac{dy}{dx}+2xy=5y^{3}
derivative of 6ln(x^2)	\frac{d}{dx}(6\ln(x^{2}))
integral of x*tan^2(x)	\int\:x\cdot\:\tan^{2}(x)dx
limit as x approaches 0 of sqrt(3x+1)	\lim\:_{x\to\:0}(\sqrt{3x+1})
(y^'-e^{-t}+3)/y =-3	\frac{y^{\prime\:}-e^{-t}+3}{y}=-3
limit as n approaches infinity of \sum_{i=1}^n(1+(2i)/n)^3(2/n)	\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}(1+\frac{2i}{n})^{3}(\frac{2}{n}))
derivative of (x^3+x-2/(x-x^2))	\frac{d}{dx}(\frac{x^{3}+x-2}{x-x^{2}})
derivative of e^{(1-x^2-(y^2/4)})	\frac{d}{dx}(e^{(1-x^{2}-\frac{y^{2}}{4})})
derivative of e^{3e^x}	derivative\:e^{3e^{x}}
tangent of f(x)=2x^2,\at x=-1	tangent\:f(x)=2x^{2},\at\:x=-1
derivative of (-10/(\sqrt[3]{x)})	\frac{d}{dx}(\frac{-10}{\sqrt[3]{x}})
integral from 2 to 6 of (1/(sqrt(x-2)))	\int\:_{2}^{6}(\frac{1}{\sqrt{x-2}})dx
limit as x approaches 1 of ln\|ln(x)\|	\lim\:_{x\to\:1}(\ln\left\|\ln(x)\right\|)
(dy)/(dt)=8y	\frac{dy}{dt}=8y
(dy)/(dx)=x^3+2x+pi	\frac{dy}{dx}=x^{3}+2x+π
integral from-1 to 2 of (-x^2+x+2)	\int\:_{-1}^{2}(-x^{2}+x+2)dx
derivative of tan(x^3)	\frac{d}{dx}(\tan(x^{3}))
derivative of (sin^2(x))/(cos^2(x))	derivative\:\frac{\sin^{2}(x)}{\cos^{2}(x)}
limit as x approaches 4+of 2x-7	\lim\:_{x\to\:4+}(2x-7)
slope of sqrt(x)+1/(sqrt(x^3))	slope\:\sqrt{x}+\frac{1}{\sqrt{x^{3}}}

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