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Popular Calculus Problems

limit as x approaches 16 of (sin(x))/x	\lim\:_{x\to\:16}(\frac{\sin(x)}{x})
xy^'-2y=-2x^2+2x-2	xy^{\prime\:}-2y=-2x^{2}+2x-2
integral from 0 to 4 of (2x+4)	\int\:_{0}^{4}(2x+4)dx
tangent of (2x^2+1)3(x^2-4)2	tangent\:(2x^{2}+1)3(x^{2}-4)2
integral of (cos^2(x)sin(x))/2	\int\:\frac{\cos^{2}(x)\sin(x)}{2}dx
limit as x approaches pi of ln(cos(x)-4)	\lim\:_{x\to\:π}(\ln(\cos(x)-4))
y^{''}-4y^'-12y=sin(2t)	y^{\prime\:\prime\:}-4y^{\prime\:}-12y=\sin(2t)
integral of (2x+3)/((x^2+3x+1)^3)	\int\:\frac{2x+3}{(x^{2}+3x+1)^{3}}dx
integral of (ln(x^{18}))/x	\int\:\frac{\ln(x^{18})}{x}dx
integral of (2x^3-4x+3x)	\int\:(2x^{3}-4x+3x)dx
(\partial)/(\partial y)((x^2y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}y}{x^{2}+y^{2}})
(dy)/(dx)=(e^{-2x})/(1+e^{-2x)}	\frac{dy}{dx}=\frac{e^{-2x}}{1+e^{-2x}}
derivative of 10cos(x)	derivative\:10\cos(x)
integral of xe^{-1/2 x^2}	\int\:xe^{-\frac{1}{2}x^{2}}dx
limit as x approaches-infinity of e^{ax}	\lim\:_{x\to\:-\infty\:}(e^{ax})
maclaurin e^{(-x^2)/2}	maclaurin\:e^{\frac{-x^{2}}{2}}
integral of 1/(x(x^2-8))	\int\:\frac{1}{x(x^{2}-8)}dx
derivative of f(x)=x(x+1)^{1/3}	derivative\:f(x)=x(x+1)^{\frac{1}{3}}
(dx)/(dt)= 1/(x+t+1)	\frac{dx}{dt}=\frac{1}{x+t+1}
slope of (2,1),(5,7)	slope\:(2,1),(5,7)
integral of (2e^{2x})/(e^{2x)+12e^x+35}	\int\:\frac{2e^{2x}}{e^{2x}+12e^{x}+35}dx
derivative of 6-arcsin(x/(x^2+4))	\frac{d}{dx}(6-\arcsin(\frac{x}{x^{2}+4}))
integral of (3x^2-4x^3)	\int\:(3x^{2}-4x^{3})dx
xy^'+3y^'-(x+3)cos(x)+y=0	xy^{\prime\:}+3y^{\prime\:}-(x+3)\cos(x)+y=0
integral of (1-y)^3	\int\:(1-y)^{3}dy
integral of ycos(4y)	\int\:y\cos(4y)dy
derivative of y=((2x^2-1)^3)/((5x-8)^2)	derivative\:y=\frac{(2x^{2}-1)^{3}}{(5x-8)^{2}}
(\partial)/(\partial x)(xsqrt(x+1))	\frac{\partial\:}{\partial\:x}(x\sqrt{x+1})
(dy)/(dx)=2y	\frac{dy}{dx}=2y
integral from 0 to 6 of 3x-x^2	\int\:_{0}^{6}3x-x^{2}dx
derivative of 1/(x-3)	derivative\:\frac{1}{x-3}
limit as x approaches 0-of cos(x)	\lim\:_{x\to\:0-}(\cos(x))
integral of xcos^4(x)	\int\:x\cos^{4}(x)dx
integral of ((x+5)/(sqrt(x)))	\int\:(\frac{x+5}{\sqrt{x}})dx
sum from n=0 to infinity of 1-cos(1/n)	\sum\:_{n=0}^{\infty\:}1-\cos(\frac{1}{n})
y^{''}-6y^'+9y=((e^{3t}))/(t^2)	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=\frac{(e^{3t})}{t^{2}}
derivative of f(x)=(2x^2+2x-4)/(x^2+x-6)	derivative\:f(x)=\frac{2x^{2}+2x-4}{x^{2}+x-6}
derivative of 2(e^{-x}-e^{-x}x)	\frac{d}{dx}(2(e^{-x}-e^{-x}x))
limit as x approaches infinity of x/(28)	\lim\:_{x\to\:\infty\:}(\frac{x}{28})
(\partial)/(\partial x)(5x^3y^6)	\frac{\partial\:}{\partial\:x}(5x^{3}y^{6})
(\partial)/(\partial x)(2y-x)	\frac{\partial\:}{\partial\:x}(2y-x)
laplacetransform 6-t	laplacetransform\:6-t
derivative of (-(x+1)/((x-1)^3))	\frac{d}{dx}(\frac{-(x+1)}{(x-1)^{3}})
integral of cos^4(7x+3)	\int\:\cos^{4}(7x+3)dx
(dy)/(dx)=4y+a	\frac{dy}{dx}=4y+a
laplacetransform t^2e^{-4t}	laplacetransform\:t^{2}e^{-4t}
derivative of sqrt(x^5)	derivative\:\sqrt{x^{5}}
maclaurin sin(pi*x)	maclaurin\:\sin(π\cdot\:x)
slope of (10,6),(1,-8)	slope\:(10,6),(1,-8)
(\partial)/(\partial x)(y^2sqrt(x))	\frac{\partial\:}{\partial\:x}(y^{2}\sqrt{x})
(\partial)/(\partial x)(cos(y)-sin(x))	\frac{\partial\:}{\partial\:x}(\cos(y)-\sin(x))
integral of 2(x-3)^3	\int\:2(x-3)^{3}dx
(d^2y)/(dx^2)+4y=sin(2)	\frac{d^{2}y}{dx^{2}}+4y=\sin(2)
integral of xe^{y^3}	\int\:xe^{y^{3}}dy
tangent of P=x^3-5x,(1,-4)	tangent\:P=x^{3}-5x,(1,-4)
derivative of cos((1-e^{8x})/(1+e^{8x)})	derivative\:\cos(\frac{1-e^{8x}}{1+e^{8x}})
derivative of f(x)=(x^2+3x+5)e^{6x}	derivative\:f(x)=(x^{2}+3x+5)e^{6x}
d/(dt)(2-2t)	\frac{d}{dt}(2-2t)
integral of (csc^2(x))/(cot^2(x))	\int\:\frac{\csc^{2}(x)}{\cot^{2}(x)}dx
integral from 0 to 2 of (e^x)/(1+e^x)	\int\:_{0}^{2}\frac{e^{x}}{1+e^{x}}dx
(dy}{dx}=\frac{x+1)/y	\frac{dy}{dx}=\frac{x+1}{y}
30y^{''}-19y^'-5y=0	30y^{\prime\:\prime\:}-19y^{\prime\:}-5y=0
limit as x approaches 7 of 4/((x-7)^2)	\lim\:_{x\to\:7}(\frac{4}{(x-7)^{2}})
integral of tan(x^3)x^2	\int\:\tan(x^{3})x^{2}dx
derivative of (9x)/(e^x)	derivative\:\frac{9x}{e^{x}}
limit as x approaches infinity of x+a	\lim\:_{x\to\:\infty\:}(x+a)
derivative of f(t)= 7/(sqrt(t))	derivative\:f(t)=\frac{7}{\sqrt{t}}
y^'+3xy^3=0,y(0)=1	y^{\prime\:}+3xy^{3}=0,y(0)=1
derivative of (x+1/x)^5	derivative\:(x+\frac{1}{x})^{5}
(dy)/(dx)=2x^{-3}	\frac{dy}{dx}=2x^{-3}
limit as x approaches 2 of sqrt(14+x)	\lim\:_{x\to\:2}(\sqrt{14+x})
(\partial)/(\partial x)(e^ysin(x)y)	\frac{\partial\:}{\partial\:x}(e^{y}\sin(x)y)
taylor 2xe^{-4x}	taylor\:2xe^{-4x}
4y^{''}-4y^'+y=16e^{(t/2)}	4y^{\prime\:\prime\:}-4y^{\prime\:}+y=16e^{(\frac{t}{2})}
integral of 1-1/(x^2)	\int\:1-\frac{1}{x^{2}}dx
integral of 7x^2e^{6x}	\int\:7x^{2}e^{6x}dx
derivative of (x^{-2}+x)^{-3}	derivative\:(x^{-2}+x)^{-3}
tangent of f(x)=(x+2sin(x))	tangent\:f(x)=(x+2\sin(x))
integral of (x-3)/(sqrt(3-4x^2))	\int\:\frac{x-3}{\sqrt{3-4x^{2}}}dx
derivative of (4X-1)^2(3X-1)^{-2}	derivative\:(4X-1)^{2}(3X-1)^{-2}
(dy)/(dx)=8xy	\frac{dy}{dx}=8xy
integral of x/(sqrt(196x^2-1))	\int\:\frac{x}{\sqrt{196x^{2}-1}}dx
integral of (x+1)/((x^2+2x-3)^2)	\int\:\frac{x+1}{(x^{2}+2x-3)^{2}}dx
integral of x^2-7	\int\:x^{2}-7dx
integral from 1 to 4 of (1-x)(x-4)	\int\:_{1}^{4}(1-x)(x-4)dx
derivative of x/((1-x^3))	\frac{d}{dx}(\frac{x}{(1-x)^{3}})
y^{''}-2y^'+y=(e^t)/((1+t^2))	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{e^{t}}{(1+t^{2})}
integral of 1/x e^{-x}	\int\:\frac{1}{x}e^{-x}dx
sum from n=0 to infinity of cos(5npi)	\sum\:_{n=0}^{\infty\:}\cos(5nπ)
f(x)=ln^5(x)	f(x)=\ln^{5}(x)
y^'-4y=10sin(2t)	y^{\prime\:}-4y=10\sin(2t)
integral of (2/(y+1))^2	\int\:(\frac{2}{y+1})^{2}dy
tangent of f(x)=x^2-8,(-2,-4)	tangent\:f(x)=x^{2}-8,(-2,-4)
inverse oflaplace 4/((s^4+4))	inverselaplace\:\frac{4}{(s^{4}+4)}
integral from 2 to infinity of xe^{-9x}	\int\:_{2}^{\infty\:}xe^{-9x}dx
limit as x approaches 4 of sqrt(4-x)	\lim\:_{x\to\:4}(\sqrt{4-x})
tangent of 1/(x-7)	tangent\:\frac{1}{x-7}
integral of 7/(3x)	\int\:\frac{7}{3x}dx
(\partial)/(\partial t)(2s^2+t^2)	\frac{\partial\:}{\partial\:t}(2s^{2}+t^{2})
integral of 1/(\sqrt[3]{x+1)}	\int\:\frac{1}{\sqrt[3]{x+1}}dx

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