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Popular Calculus Problems

integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x))	\int\:_{0}^{9}\frac{11e^{\sqrt{x}}}{\sqrt{x}}dx
(dy)/(dt)=t^2y^2	\frac{dy}{dt}=t^{2}y^{2}
integral of cos^2(15x)	\int\:\cos^{2}(15x)dx
integral of 2/(5x-1)	\int\:\frac{2}{5x-1}dx
(\partial)/(\partial y)(sqrt(3x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{3x^{2}+y^{2}})
derivative of 6sqrt(x^7)	\frac{d}{dx}(6\sqrt{x^{7}})
derivative of 3ax+bx^3	\frac{d}{dx}(3ax+bx^{3})
(\partial)/(\partial x)(3x^2+5xy-7y^2+1)	\frac{\partial\:}{\partial\:x}(3x^{2}+5xy-7y^{2}+1)
derivative of e^{x^2+4}	\frac{d}{dx}(e^{x^{2}+4})
integral of x^2(6-x^3)	\int\:x^{2}(6-x^{3})dx
derivative of cos^2(2x+1)	\frac{d}{dx}(\cos^{2}(2x+1))
integral of 3/5	\int\:\frac{3}{5}dx
(\partial)/(\partial x)(x^2+y^2+z^2-2yz)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2}-2yz)
derivative of d{y}(d,x)	\frac{d}{dx}(d{y}(d,x))
taylor 7/(sqrt(x)),4	taylor\:\frac{7}{\sqrt{x}},4
integral from 1 to 4 of sqrt(x)ln(x/2)	\int\:_{1}^{4}\sqrt{x}\ln(\frac{x}{2})dx
y^{'''}-6y^{''}+11y^'-6y=0	y^{\prime\:\prime\:\prime\:}-6y^{\prime\:\prime\:}+11y^{\prime\:}-6y=0
integral from-5 to 1 of (2x+6)	\int\:_{-5}^{1}(2x+6)dx
derivative of (sqrt(7))/t	derivative\:\frac{\sqrt{7}}{t}
laplacetransform 1/2 t^2	laplacetransform\:\frac{1}{2}t^{2}
area y=2x-1,x=2,x=5,y=0	area\:y=2x-1,x=2,x=5,y=0
(dx)/(dt)=e^{3t+2x}	\frac{dx}{dt}=e^{3t+2x}
derivative of-1/3 ln((tan(x/2-3)/3))	\frac{d}{dx}(-\frac{1}{3}\ln(\frac{\tan(\frac{x}{2})-3}{3}))
y^{''}+6y^'+8y=130cos(3t)	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=130\cos(3t)
limit as x approaches-1/e of xln(e+1/x)	\lim\:_{x\to\:-\frac{1}{e}}(x\ln(e+\frac{1}{x}))
integral of xsqrt(1-2x)	\int\:x\sqrt{1-2x}dx
(\partial)/(\partial x)(x/(e^{x/y)})	\frac{\partial\:}{\partial\:x}(\frac{x}{e^{\frac{x}{y}}})
derivative of-2/((6x-7x^4^3))	\frac{d}{dx}(-\frac{2}{(6x-7x^{4})^{3}})
(dy)/(dx)=log_{10}(x)	\frac{dy}{dx}=\log_{10}(x)
(dy}{dx}=\frac{x^9-8y)/x	\frac{dy}{dx}=\frac{x^{9}-8y}{x}
derivative of \|4x-20\|	\frac{d}{dx}(\left\|4x-20\right\|)
integral from 6 to 12 of 2x-18	\int\:_{6}^{12}2x-18dx
integral of (5x+2)^3	\int\:(5x+2)^{3}dx
y^{''}+y=e^x	y^{\prime\:\prime\:}+y=e^{x}
(dy)/(dx)=((x^2-1))/(2y),y(3)=1	\frac{dy}{dx}=\frac{(x^{2}-1)}{2y},y(3)=1
(\partial)/(\partial y)(y^2e^{xyz})	\frac{\partial\:}{\partial\:y}(y^{2}e^{xyz})
(\partial)/(\partial x)(y^5-4xy)	\frac{\partial\:}{\partial\:x}(y^{5}-4xy)
y^'=(6y^3)/((3-2x)^2),y(0)=-1	y^{\prime\:}=\frac{6y^{3}}{(3-2x)^{2}},y(0)=-1
integral from 0 to 1 of ln(2x)	\int\:_{0}^{1}\ln(2x)dx
integral of (2/(x^2))	\int\:(\frac{2}{x^{2}})dx
(\partial)/(\partial x)(1/x-y/x)	\frac{\partial\:}{\partial\:x}(\frac{1}{x}-\frac{y}{x})
integral of tan^2(x)tan(x)	\int\:\tan^{2}(x)\tan(x)dx
integral of 7/((x-3)sqrt(x^2-6x+5))	\int\:\frac{7}{(x-3)\sqrt{x^{2}-6x+5}}dx
(\partial)/(\partial x)(e^{-x}sin(x))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(x))
derivative of 8/(x-5)	\frac{d}{dx}(\frac{8}{x-5})
f(x)=-csc^2(x)	f(x)=-\csc^{2}(x)
(x^2-y^2)dx+(2xy)dy=0	(x^{2}-y^{2})dx+(2xy)dy=0
integral of 1/(sqrt(-x^2+4x-3))	\int\:\frac{1}{\sqrt{-x^{2}+4x-3}}dx
integral of 15/4 x^2	\int\:\frac{15}{4}x^{2}dx
d/(dt)(log_{3}(2t-x))	\frac{d}{dt}(\log_{3}(2t-x))
tangent of y=2x^3+3x^2-12x+1	tangent\:y=2x^{3}+3x^{2}-12x+1
d/(d{r)}(sqrt({r)}+\sqrt[3]{{r}})	\frac{d}{d{r}}(\sqrt{{r}}+\sqrt[3]{{r}})
(\partial)/(\partial y)((2y)/(x^2-y^2))	\frac{\partial\:}{\partial\:y}(\frac{2y}{x^{2}-y^{2}})
derivative of cos(xsin(x))	derivative\:\cos(x\sin(x))
derivative of (-6x/(1-x))	\frac{d}{dx}(\frac{-6x}{1-x})
inverse oflaplace (s+4)/(s^2+6s+18)	inverselaplace\:\frac{s+4}{s^{2}+6s+18}
integral of ax^5	\int\:ax^{5}dx
area y=x^2,y=8-x^2,y=4x+11	area\:y=x^{2},y=8-x^{2},y=4x+11
limit as x approaches 3 of (x-2)^2	\lim\:_{x\to\:3}((x-2)^{2})
(dy)/(dx)= k/(x^2)	\frac{dy}{dx}=\frac{k}{x^{2}}
integral from 1 to 2 of (3ln(x))/(x^2)	\int\:_{1}^{2}\frac{3\ln(x)}{x^{2}}dx
(\partial)/(\partial x)(2y^2-3x^2-z)	\frac{\partial\:}{\partial\:x}(2y^{2}-3x^{2}-z)
derivative of log_{e}(sqrt(x^2+1))	\frac{d}{dx}(\log_{e}(\sqrt{x^{2}+1}))
derivative of y=(tan(-1(3x)))2	derivative\:y=(\tan(-1(3x)))2
derivative of \sqrt[x]{x}	derivative\:\sqrt[x]{x}
derivative of-0.6t^2+30t	derivative\:-0.6t^{2}+30t
integral from 0 to 5 of pi(-3/5 x+3)^2	\int\:_{0}^{5}π(-\frac{3}{5}x+3)^{2}dx
derivative of (t^3+3t)/(t^2-4t+3)	derivative\:\frac{t^{3}+3t}{t^{2}-4t+3}
integral of 7/(x(x-7)^2)	\int\:\frac{7}{x(x-7)^{2}}dx
derivative of (x-100^3+(x-100)^2+500)	\frac{d}{dx}((x-100)^{3}+(x-100)^{2}+500)
integral of sqrt(1-y^2)	\int\:\sqrt{1-y^{2}}dy
derivative of (x^3+7^{2/3})	\frac{d}{dx}((x^{3}+7)^{\frac{2}{3}})
derivative of g(x)=sqrt(8-x)	derivative\:g(x)=\sqrt{8-x}
tangent of f(x)=(5x-1)^{-1/6},\at x=13	tangent\:f(x)=(5x-1)^{-\frac{1}{6}},\at\:x=13
limit as x approaches 0+of (1/x)^{3x}	\lim\:_{x\to\:0+}((\frac{1}{x})^{3x})
tangent of y=2x^2+x,(1,2)	tangent\:y=2x^{2}+x,(1,2)
integral from 5 to 2 of x	\int\:_{5}^{2}xdx
y^'+10y=10	y^{\prime\:}+10y=10
integral of x/(x^2+3x+9)	\int\:\frac{x}{x^{2}+3x+9}dx
integral of 2x^{-3}	\int\:2x^{-3}dx
integral from 0 to 4 of (2t)/((t-5)^2)	\int\:_{0}^{4}\frac{2t}{(t-5)^{2}}dt
limit as x approaches 0 of ln(1+x)	\lim\:_{x\to\:0}(\ln(1+x))
(\partial)/(\partial z)(8x^{y/z})	\frac{\partial\:}{\partial\:z}(8x^{\frac{y}{z}})
laplacetransform 3(t-2)^2+13(t-2)+17	laplacetransform\:3(t-2)^{2}+13(t-2)+17
sum from n=0 to infinity of n(1-p)^{n-1}	\sum\:_{n=0}^{\infty\:}n(1-p)^{n-1}
integral from 1 to 3 of 1/x	\int\:_{1}^{3}\frac{1}{x}dx
integral of (14x^2+8x-5)/(x^3+x^2)	\int\:\frac{14x^{2}+8x-5}{x^{3}+x^{2}}dx
d/(dt)((e^{-t}-e^{-t}t)/(e^t))	\frac{d}{dt}(\frac{e^{-t}-e^{-t}t}{e^{t}})
sum from n=0 to infinity of n(2/3)^n	\sum\:_{n=0}^{\infty\:}n(\frac{2}{3})^{n}
derivative of cos(x-xsin(x))	\frac{d}{dx}(\cos(x)-x\sin(x))
derivative of f(x)=x^2e^{-x^2}	derivative\:f(x)=x^{2}e^{-x^{2}}
integral of (4x+1)/(x(x^2-2x+1))	\int\:\frac{4x+1}{x(x^{2}-2x+1)}dx
derivative of x*(1-x)	derivative\:x\cdot\:(1-x)
(\partial)/(\partial y)(sin(xy))	\frac{\partial\:}{\partial\:y}(\sin(xy))
integral of (a+sqrt(x))^2	\int\:(a+\sqrt{x})^{2}dx
derivative of ((x^2-1^3)/4)	\frac{d}{dx}(\frac{(x^{2}-1)^{3}}{4})
sum from n=0 to infinity of (e^n)/(n^n)	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{n^{n}}
(\partial)/(\partial y)(sin(x^2)-y)	\frac{\partial\:}{\partial\:y}(\sin(x^{2})-y)
derivative of 2sin(sqrt(x))	\frac{d}{dx}(2\sin(\sqrt{x}))
derivative of arcsin(2/3)	derivative\:\arcsin(\frac{2}{3})

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