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Popular Calculus Problems

(dy)/(dt)-2ty=3t^2e^{t^2}	\frac{dy}{dt}-2ty=3t^{2}e^{t^{2}}
integral from 0 to pi of cos^2(t)	\int\:_{0}^{π}\cos^{2}(t)dt
derivative of f(x)=x^{e^x}	derivative\:f(x)=x^{e^{x}}
integral of (x^2y^3-1/(1+9x^2))	\int\:(x^{2}y^{3}-\frac{1}{1+9x^{2}})dx
integral of (14x-13)/(sqrt(x^2-4x-21))	\int\:\frac{14x-13}{\sqrt{x^{2}-4x-21}}dx
(\partial)/(\partial x)((7y)/(x^2+y^2+19))	\frac{\partial\:}{\partial\:x}(\frac{7y}{x^{2}+y^{2}+19})
slope of-(18)/((x-9)^2)	slope\:-\frac{18}{(x-9)^{2}}
derivative of f(x)=sqrt(22x)	derivative\:f(x)=\sqrt{22x}
derivative of y=-6(4x^2+4)^{-6}	derivative\:y=-6(4x^{2}+4)^{-6}
integral from 0 to infinity of arctan(x)	\int\:_{0}^{\infty\:}\arctan(x)dx
(\partial)/(\partial x)(x-4)	\frac{\partial\:}{\partial\:x}(x-4)
integral of-1/2 e^{2x}	\int\:-\frac{1}{2}e^{2x}dx
(\partial)/(\partial y)(e^{3x-y})	\frac{\partial\:}{\partial\:y}(e^{3x-y})
integral of xe^{2-x}	\int\:xe^{2-x}dx
integral of 1/3 sqrt(x)	\int\:\frac{1}{3}\sqrt{x}dx
derivative of y=x^2sin(2x)	derivative\:y=x^{2}\sin(2x)
derivative of a/((x^2+a^2^2))	\frac{d}{dx}(\frac{a}{(x^{2}+a^{2})^{2}})
derivative of x^3+3x^2+3x+1	\frac{d}{dx}(x^{3}+3x^{2}+3x+1)
(\partial)/(\partial x)(3^{2x}+5^{4y}+2x+y^4)	\frac{\partial\:}{\partial\:x}(3^{2x}+5^{4y}+2x+y^{4})
derivative of (x^3+x^2e^{2x})	\frac{d}{dx}((x^{3}+x^{2})e^{2x})
integral of xsqrt(2)-1/(2sqrt(x))	\int\:x\sqrt{2}-\frac{1}{2\sqrt{x}}dx
limit as x approaches 0 of (x+6)/(x^2+3)	\lim\:_{x\to\:0}(\frac{x+6}{x^{2}+3})
integral of x^4sec^2(x^5+2)	\int\:x^{4}\sec^{2}(x^{5}+2)dx
y^'+3y=2sin(e^{3x})	y^{\prime\:}+3y=2\sin(e^{3x})
integral of sqrt(x^3)sin^2(1+x^{5/2})	\int\:\sqrt{x^{3}}\sin^{2}(1+x^{\frac{5}{2}})dx
integral from-1 to 1 of x^2-1	\int\:_{-1}^{1}x^{2}-1dx
integral from 0 to 0.5 of 750x	\int\:_{0}^{0.5}750xdx
tangent of 2e^xcos(x)	tangent\:2e^{x}\cos(x)
y^'+(1/x-1)y=-2/x	y^{\prime\:}+(\frac{1}{x}-1)y=-\frac{2}{x}
derivative of 5(2-x^3^4)	\frac{d}{dx}(5(2-x^{3})^{4})
(\partial)/(\partial x)(-3y^5sin(3x))	\frac{\partial\:}{\partial\:x}(-3y^{5}\sin(3x))
inverse oflaplace (7s+2)/(s^2+6s+34)	inverselaplace\:\frac{7s+2}{s^{2}+6s+34}
limit as n approaches infinity of e^{1/n ln(n)}	\lim\:_{n\to\:\infty\:}(e^{\frac{1}{n}\ln(n)})
derivative of 2x^3-3	\frac{d}{dx}(2x^{3}-3)
y^'= y/x ,y(1)=2	y^{\prime\:}=\frac{y}{x},y(1)=2
derivative of (2x^2-2x+2/((2x-1)^2))	\frac{d}{dx}(\frac{2x^{2}-2x+2}{(2x-1)^{2}})
slope of (4.5)(9.25)	slope\:(4.5)(9.25)
limit as x approaches-infinity of 5/x	\lim\:_{x\to\:-\infty\:}(\frac{5}{x})
integral of (14x+2)	\int\:(14x+2)dx
slope of eln(2x^4+ax^2y^2+2y^4)	slope\:e\ln(2x^{4}+ax^{2}y^{2}+2y^{4})
y^{''}-9y=(x^2-2)sin(3x)	y^{\prime\:\prime\:}-9y=(x^{2}-2)\sin(3x)
integral of-10x^{-6}	\int\:-10x^{-6}dx
integral of (3^x-x^3+e^x)	\int\:(3^{x}-x^{3}+e^{x})dx
limit as x approaches 0 of-3x^2-5x+1	\lim\:_{x\to\:0}(-3x^{2}-5x+1)
integral of (7-x^2)/(5x^3+x)	\int\:\frac{7-x^{2}}{5x^{3}+x}dx
limit as x approaches 0 of xe^{-1/x}	\lim\:_{x\to\:0}(xe^{-\frac{1}{x}})
tangent of f(x)=8sqrt(x),\at x=16	tangent\:f(x)=8\sqrt{x},\at\:x=16
derivative of log_{3}(2x^2+4x+3)	derivative\:\log_{3}(2x^{2}+4x+3)
sum from n=1 to infinity of (99^n(n^5+2))/(n^210^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{99^{n}(n^{5}+2)}{n^{2}10^{2n}}
derivative of f(x)=(11)/(ln(x))	derivative\:f(x)=\frac{11}{\ln(x)}
integral of ((2x^2-3))/((x-2)(x^2+4))	\int\:\frac{(2x^{2}-3)}{(x-2)(x^{2}+4)}dx
derivative of (6x+7(7x-8))	\frac{d}{dx}((6x+7)(7x-8))
integral of x^2x^e	\int\:x^{2}x^{e}dx
integral of 3^{5x-1}	\int\:3^{5x-1}dx
(3dy)/(dx)=y^2	\frac{3dy}{dx}=y^{2}
derivative of (sqrt(x)/(8x+8))	\frac{d}{dx}(\frac{\sqrt{x}}{8x+8})
limit as x approaches 9 of (x+8)/(x+9)	\lim\:_{x\to\:9}(\frac{x+8}{x+9})
limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2}	\lim\:_{p\to\:9}(\frac{\sqrt{p}-3}{\sqrt{1+\sqrt{p}}-2})
limit as x approaches 3+of (\|3-x\|)/(3-x)	\lim\:_{x\to\:3+}(\frac{\left\|3-x\right\|}{3-x})
integral of 2-2x	\int\:2-2xdx
derivative of 3x^2+x	\frac{d}{dx}(3x^{2}+x)
(\partial)/(\partial x)(-6+5-3y)	\frac{\partial\:}{\partial\:x}(-6+5-3y)
integral of e^x*x	\int\:e^{x}\cdot\:xdx
derivative of (216)/(x^2+36)	derivative\:\frac{216}{x^{2}+36}
integral of ra^r	\int\:ra^{r}dr
integral of (x+1)^5	\int\:(x+1)^{5}dx
derivative of [x+(x+sin^2(x)^5]^3)	\frac{d}{dx}([x+(x+\sin^{2}(x))^{5}]^{3})
integral of-(2000t)/((1+t^2))	\int\:-\frac{2000t}{(1+t^{2})}dt
derivative of 4x^2+x	\frac{d}{dx}(4x^{2}+x)
derivative of x^2-6x	derivative\:x^{2}-6x
limit as x approaches-2-of-1	\lim\:_{x\to\:-2-}(-1)
derivative of 3(x^2+3x+1)^2(2x+3)	derivative\:3(x^{2}+3x+1)^{2}(2x+3)
derivative of 2x^7	derivative\:2x^{7}
(\partial)/(\partial x)(sin(3x)cos(4y))	\frac{\partial\:}{\partial\:x}(\sin(3x)\cos(4y))
slope of (-3.1)(-17.2)	slope\:(-3.1)(-17.2)
integral from 0 to 2 of x^2e^x	\int\:_{0}^{2}x^{2}e^{x}dx
derivative of e^3	derivative\:e^{3}
integral of 9xsqrt(1+2x^2)	\int\:9x\sqrt{1+2x^{2}}dx
limit as n approaches infinity of 0	\lim\:_{n\to\:\infty\:}(0)
derivative of sqrt(7x-2)	derivative\:\sqrt{7x-2}
derivative of (x-2^2(x+4))	\frac{d}{dx}((x-2)^{2}(x+4))
(4x(-9)^')^'	(4x(-9)^{\prime\:})^{\prime\:}
taylor 4x*ln(x)	taylor\:4x\cdot\:\ln(x)
limit as x approaches-3 of sqrt(36-6x)	\lim\:_{x\to\:-3}(\sqrt{36-6x})
integral from-1 to 1 of 4/x	\int\:_{-1}^{1}\frac{4}{x}dx
(\partial)/(\partial x)(x^{1/8}*y^{11/9})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{8}}\cdot\:y^{\frac{11}{9}})
integral of (x^5)/((1-x^3)^{3/2)}	\int\:\frac{x^{5}}{(1-x^{3})^{\frac{3}{2}}}dx
(\partial)/(\partial x)(sqrt(1-(x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\sqrt{1-(x^{2}+y^{2})})
(x-y)dx-xdy=0	(x-y)dx-xdy=0
integral of x^3sqrt(x^2+3)	\int\:x^{3}\sqrt{x^{2}+3}dx
integral from 0 to 1 of (x-1)/(x+1)	\int\:_{0}^{1}\frac{x-1}{x+1}dx
integral from 1 to 4 of (5-2t+3t^2)	\int\:_{1}^{4}(5-2t+3t^{2})dt
integral of 3x^2cos(x^3)	\int\:3x^{2}\cos(x^{3})dx
derivative of f(x)=5e^{4x}	derivative\:f(x)=5e^{4x}
x(dy)/(dx)+2y=-3e^x	x\frac{dy}{dx}+2y=-3e^{x}
derivative of 7-4x	\frac{d}{dx}(7-4x)
integral of 2x^{-4}	\int\:2x^{-4}dx
derivative of sin(x^2+1)	derivative\:\sin(x^{2}+1)
derivative of x/((x-3^2))	\frac{d}{dx}(\frac{x}{(x-3)^{2}})
y^{''}+9y^'+18y=0	y^{\prime\:\prime\:}+9y^{\prime\:}+18y=0

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