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Popular Calculus Problems

y^{''}-3y^'=8x	y^{\prime\:\prime\:}-3y^{\prime\:}=8x
limit as x approaches 4+of x/(x-4)	\lim\:_{x\to\:4+}(\frac{x}{x-4})
inverse oflaplace 1/(3s+2)	inverselaplace\:\frac{1}{3s+2}
(d^2)/(dx^2)((x^2)/(1+x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{1+x})
derivative of (5x)/(x+2)	derivative\:\frac{5x}{x+2}
derivative of 7x^3	derivative\:7x^{3}
(\partial)/(\partial x)(cos(x)+sin(y))	\frac{\partial\:}{\partial\:x}(\cos(x)+\sin(y))
integral of x^6ln(2x)	\int\:x^{6}\ln(2x)dx
(dy)/(dt)=3y+y^6	\frac{dy}{dt}=3y+y^{6}
derivative of f(x)=(2-xe^x)/(x+e^x)	derivative\:f(x)=\frac{2-xe^{x}}{x+e^{x}}
taylor e^x*cos(x)	taylor\:e^{x}\cdot\:\cos(x)
integral from-1 to 1 of (1/(1+x^2))^2	\int\:_{-1}^{1}(\frac{1}{1+x^{2}})^{2}dx
integral of (3x^3-4x^2+3x)/(x^2+1)	\int\:\frac{3x^{3}-4x^{2}+3x}{x^{2}+1}dx
integral of 6x^5-7x^4-9x^2	\int\:6x^{5}-7x^{4}-9x^{2}dx
integral of x+c	\int\:x+cdx
integral from 0 to 1 of integral from 0 to x of (6/7 (x^2+x*y/2))	\int\:_{0}^{1}\int\:_{0}^{x}(\frac{6}{7}(x^{2}+x\cdot\:\frac{y}{2}))dydx
derivative of y= t/((t-7)^2)	derivative\:y=\frac{t}{(t-7)^{2}}
limit as x approaches infinity of ln(9x)-ln(x+7)	\lim\:_{x\to\:\infty\:}(\ln(9x)-\ln(x+7))
integral of 1/(ln(x)x)	\int\:\frac{1}{\ln(x)x}dx
integral of (ln(x))/(2x)	\int\:\frac{\ln(x)}{2x}dx
derivative of f(x)=(1n(x^3))	derivative\:f(x)=(1n(x^{3}))
limit as x approaches 19 of (x-19)/(x^2-361)	\lim\:_{x\to\:19}(\frac{x-19}{x^{2}-361})
integral of e^xsqrt(31+e^x)	\int\:e^{x}\sqrt{31+e^{x}}dx
(dy)/(dx)=e^{2x}-3y,y(0)=2	\frac{dy}{dx}=e^{2x}-3y,y(0)=2
(\partial)/(\partial x)(x^5+y^3)	\frac{\partial\:}{\partial\:x}(x^{5}+y^{3})
y^{''}+2y^'+y=16e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=16e^{-t}
derivative of sqrt(2x+1)	derivative\:\sqrt{2x+1}
integral from-2 to 3 of (37)/(x^4)	\int\:_{-2}^{3}\frac{37}{x^{4}}dx
limit as x approaches 0 of (20sin(3x))/x	\lim\:_{x\to\:0}(\frac{20\sin(3x)}{x})
integral of 1/((x-2)^{1/3)}	\int\:\frac{1}{(x-2)^{\frac{1}{3}}}dx
limit as h approaches 0 of ((sqrt(5(x+h)+4))-sqrt(5x+4))/h	\lim\:_{h\to\:0}(\frac{(\sqrt{5(x+h)+4})-\sqrt{5x+4}}{h})
area 4x+3,[0,1]	area\:4x+3,[0,1]
integral of (3x^3-2x^2+6x)/x	\int\:\frac{3x^{3}-2x^{2}+6x}{x}dx
integral of e^xcos(y)-x-2	\int\:e^{x}\cos(y)-x-2
(sech(2x))^{sin(3x)}	(\sech(2x))^{\sin(3x)}
integral of csc(x)	\int\:\csc(x)dx
derivative of 1+cos^2(x)	derivative\:1+\cos^{2}(x)
(dx)/(dy)2-(dy)/(dx)sec(x)=0	\frac{dx}{dy}2-\frac{dy}{dx}\sec(x)=0
derivative of f(x)= 2/(5x+3)	derivative\:f(x)=\frac{2}{5x+3}
sum from n=1 to infinity}((-1)^{n-1 of)/(4n+1)	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n-1}}{4n+1}
derivative of (3x-2^2(2x+1)^4)	\frac{d}{dx}((3x-2)^{2}(2x+1)^{4})
(\partial)/(\partial x)(4x^2+4y^2)	\frac{\partial\:}{\partial\:x}(4x^{2}+4y^{2})
(\partial)/(\partial y)(1000+11x+6y+xy-(x-3)^2-(y-4)^2)	\frac{\partial\:}{\partial\:y}(1000+11x+6y+xy-(x-3)^{2}-(y-4)^{2})
integral from 0 to 3 of 4/(x^2)	\int\:_{0}^{3}\frac{4}{x^{2}}dx
integral of sqrt(5x+2)	\int\:\sqrt{5x+2}dx
d/(dt)(25-25e^{-t}cos(t)-25e^{-t}sin(t))	\frac{d}{dt}(25-25e^{-t}\cos(t)-25e^{-t}\sin(t))
(\partial)/(\partial v)(e^{{u}(v)+v})	\frac{\partial\:}{\partial\:v}(e^{{u}(v)+v})
integral from 2 to 9 of (x^3-pix^2)	\int\:_{2}^{9}(x^{3}-πx^{2})dx
tangent of f(x)=8(e^x+e^xx),\at x=0	tangent\:f(x)=8(e^{x}+e^{x}x),\at\:x=0
x^2y^'+3xy=(sin(2x))/x	x^{2}y^{\prime\:}+3xy=\frac{\sin(2x)}{x}
integral of (sqrt(x^2+25))/(9x^2)	\int\:\frac{\sqrt{x^{2}+25}}{9x^{2}}dx
limit as x approaches 1+of (x+5)/(x+2)	\lim\:_{x\to\:1+}(\frac{x+5}{x+2})
(\partial)/(\partial x)(ln(4y))	\frac{\partial\:}{\partial\:x}(\ln(4y))
y^{''}-5y^'+4y=-sin(5t)	y^{\prime\:\prime\:}-5y^{\prime\:}+4y=-\sin(5t)
y^'= x/((1+2y))	y^{\prime\:}=\frac{x}{(1+2y)}
area sqrt(x),x-2,[0,4]	area\:\sqrt{x},x-2,[0,4]
(d^3)/(dx^3)(3t^3-2/(t^2))	\frac{d^{3}}{dx^{3}}(3t^{3}-\frac{2}{t^{2}})
integral of (x^3+x+1/(x^3))	\int\:(x^{3}+x+\frac{1}{x^{3}})dx
integral from 0 to pi/2 of-10sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-10\sin^{2}(3x)dx
integral of x/((sqrt(1+2x)))	\int\:\frac{x}{(\sqrt{1+2x})}dx
derivative of tan(6x^2)	\frac{d}{dx}(\tan(6x^{2}))
(\partial)/(\partial x)(cos^2(x-y))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x-y))
derivative of (x^2/(x-2))	\frac{d}{dx}(\frac{x^{2}}{x-2})
integral from 4 to 6 of 2x	\int\:_{4}^{6}2xdx
d/(dt)(\sqrt[5]{t})	\frac{d}{dt}(\sqrt[5]{t})
area x^3-4x^2+4x,[0,3]	area\:x^{3}-4x^{2}+4x,[0,3]
derivative of (1/x ^2)	\frac{d}{dx}((\frac{1}{x})^{2})
derivative of-2x^2+4x-4	\frac{d}{dx}(-2x^{2}+4x-4)
integral of 1/(sqrt(16-x))	\int\:\frac{1}{\sqrt{16-x}}dx
integral from-infinity to 0 of 1/(2-6x)	\int\:_{-\infty\:}^{0}\frac{1}{2-6x}dx
(\partial)/(\partial y)(3.5xycos(xyz))	\frac{\partial\:}{\partial\:y}(3.5xy\cos(xyz))
integral of 1/(9x^2-1)	\int\:\frac{1}{9x^{2}-1}dx
integral of 12x^2+2x-6	\int\:12x^{2}+2x-6dx
integral of 9arctan(x)	\int\:9\arctan(x)dx
(\partial)/(\partial y)(7y-5x)	\frac{\partial\:}{\partial\:y}(7y-5x)
limit as x approaches infinity of log_{10}(2x)	\lim\:_{x\to\:\infty\:}(\log_{10}(2x))
limit as x approaches-1 of (x^2-x)/(x+1)	\lim\:_{x\to\:-1}(\frac{x^{2}-x}{x+1})
derivative of 9sec(x)	\frac{d}{dx}(9\sec(x))
(\partial)/(\partial y)(ln(e^x+xy^3))	\frac{\partial\:}{\partial\:y}(\ln(e^{x}+xy^{3}))
derivative of x^4	\frac{d}{dx}(x^{4})
f(t)=(1.05)/(1+100e^{-0.285t)}	f(t)=\frac{1.05}{1+100e^{-0.285t}}
derivative of e^{1/x ln(x})	\frac{d}{dx}(e^{\frac{1}{x}\ln(x)})
slope of (3,-8),(12,-15)	slope\:(3,-8),(12,-15)
(dy)/(dx)=-x/(4y)	\frac{dy}{dx}=-\frac{x}{4y}
derivative of x^2*y	\frac{d}{dx}(x^{2}\cdot\:y)
integral from 0 to 1 of 4/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{4}{\sqrt{x}(x+1)}dx
area y=4(x+1),y=5(x+1),x=2	area\:y=4(x+1),y=5(x+1),x=2
derivative of 3x^2y^2	\frac{d}{dx}(3x^{2}y^{2})
derivative of x(1-x^2^{1/2})	\frac{d}{dx}(x(1-x^{2})^{\frac{1}{2}})
sum from n=0 to infinity of i(-1)^n	\sum\:_{n=0}^{\infty\:}i(-1)^{n}
(x+sqrt(x))(dy)/(dx)=y+sqrt(y)	(x+\sqrt{x})\frac{dy}{dx}=y+\sqrt{y}
derivative of 4arccos(sqrt(1-x^2))	\frac{d}{dx}(4\arccos(\sqrt{1-x^{2}}))
(\partial)/(\partial y)(-2y^2)	\frac{\partial\:}{\partial\:y}(-2y^{2})
integral of x\sqrt[5]{x-1}	\int\:x\sqrt[5]{x-1}dx
integral from-2 to 3 of (39)/(x^4)	\int\:_{-2}^{3}\frac{39}{x^{4}}dx
f(θ)=cos(θ^2)	f(θ)=\cos(θ^{2})
(\partial)/(\partial x)(ln(y^2))	\frac{\partial\:}{\partial\:x}(\ln(y^{2}))
y^{''}+by(x)=0	y^{\prime\:\prime\:}+by(x)=0
tangent of g(x)=x^2+3x	tangent\:g(x)=x^{2}+3x
derivative of sqrt(1+1/(x^4))	\frac{d}{dx}(\sqrt{1+\frac{1}{x^{4}}})

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