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Popular Calculus Problems

integral of 5/(3+x^2)	\int\:\frac{5}{3+x^{2}}dx
derivative of f(x)=x^2-5x+5	derivative\:f(x)=x^{2}-5x+5
slope ofintercept (6,5),(-3,-4)	slopeintercept\:(6,5),(-3,-4)
d/(dt)(3sin(t))	\frac{d}{dt}(3\sin(t))
integral of tan(x)	\int\:\tan(x)dx
slope of y=9+5x^2-2x^3	slope\:y=9+5x^{2}-2x^{3}
integral from-1 to 2 of (x-4\|x\|)	\int\:_{-1}^{2}(x-4\left\|x\right\|)dx
(\partial)/(\partial x)(x/(1+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{1+x^{2}+y^{2}})
limit as x approaches 1 of-2x^2+2k	\lim\:_{x\to\:1}(-2x^{2}+2k)
integral of 2^{cos(x)}*sin(x)	\int\:2^{\cos(x)}\cdot\:\sin(x)dx
integral of ln(x/2)	\int\:\ln(\frac{x}{2})dx
integral of xe^{3x+1}	\int\:xe^{3x+1}dx
area y=4x^2,y=4	area\:y=4x^{2},y=4
limit as x approaches 2 of-x^2+4x-2	\lim\:_{x\to\:2}(-x^{2}+4x-2)
integral of (9x^3)/(sqrt(x^2+1))	\int\:\frac{9x^{3}}{\sqrt{x^{2}+1}}dx
integral of (2x-3)/(sqrt(x^2+6x+4))	\int\:\frac{2x-3}{\sqrt{x^{2}+6x+4}}dx
derivative of 13e^x	\frac{d}{dx}(13e^{x})
tangent of f(x)=((x^2))/(x-5),\at x=-3	tangent\:f(x)=\frac{(x^{2})}{x-5},\at\:x=-3
laplacetransform 0.001t	laplacetransform\:0.001t
ty^'=4y	ty^{\prime\:}=4y
(x^2+1)y^'+4x(y-1)=0,y(0)=3	(x^{2}+1)y^{\prime\:}+4x(y-1)=0,y(0)=3
(dy)/(dx)+y^3x+8y=0	\frac{dy}{dx}+y^{3}x+8y=0
integral of sin^5(9x)	\int\:\sin^{5}(9x)dx
derivative of-2/((x-1^2))	\frac{d}{dx}(-\frac{2}{(x-1)^{2}})
sum from n=1 to infinity of 1/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{8^{n}}
(dy)/(dt)=y(7-y)-49/4	\frac{dy}{dt}=y(7-y)-\frac{49}{4}
derivative of f(x)=x^2+6x	derivative\:f(x)=x^{2}+6x
integral of 1/(sqrt(1-16x^2))	\int\:\frac{1}{\sqrt{1-16x^{2}}}dx
integral from 0 to 1 of e^{5x}-e^x	\int\:_{0}^{1}e^{5x}-e^{x}dx
derivative of e^{cot(4x)}	derivative\:e^{\cot(4x)}
integral of ((1+cos^2(x)))/(cos^2(x))	\int\:\frac{(1+\cos^{2}(x))}{\cos^{2}(x)}dx
derivative of (6x^2+8x+8x)/(sqrt(x))	derivative\:\frac{6x^{2}+8x+8x}{\sqrt{x}}
(x^2)/(y^2-2)y^'= 1/(2y),y(1)=sqrt(3)	\frac{x^{2}}{y^{2}-2}y^{\prime\:}=\frac{1}{2y},y(1)=\sqrt{3}
integral of (2x^4+3x^2-2x^{-3})/(x^2)	\int\:\frac{2x^{4}+3x^{2}-2x^{-3}}{x^{2}}dx
sum from n=1 to infinity of 1/(6n+5)	\sum\:_{n=1}^{\infty\:}\frac{1}{6n+5}
y^'=((y^2+2xy))/(x^2)	y^{\prime\:}=\frac{(y^{2}+2xy)}{x^{2}}
integral of e^{3x}sin(3x)	\int\:e^{3x}\sin(3x)dx
y^'= x/y ,y(0)=3	y^{\prime\:}=\frac{x}{y},y(0)=3
limit as x approaches-2 of 3x^2+7-1/x	\lim\:_{x\to\:-2}(3x^{2}+7-\frac{1}{x})
integral of 1/(1+(cos(x))^2)	\int\:\frac{1}{1+(\cos(x))^{2}}dx
derivative of (18x+4x^2/((9+4x)^2))	\frac{d}{dx}(\frac{18x+4x^{2}}{(9+4x)^{2}})
integral from 0 to 1 of 2+sqrt(1-x^2)	\int\:_{0}^{1}2+\sqrt{1-x^{2}}dx
derivative of (1+x^{1/x})	\frac{d}{dx}((1+x)^{\frac{1}{x}})
integral of sin(t^2)	\int\:\sin(t^{2})dt
tangent of f(x)=4x^2-5x,\at x=3	tangent\:f(x)=4x^{2}-5x,\at\:x=3
derivative of f(x)=-4x	derivative\:f(x)=-4x
(\partial)/(\partial y)(t/(2y^4))	\frac{\partial\:}{\partial\:y}(\frac{t}{2y^{4}})
integral of xsin(5x^2)cos(6x^2)	\int\:x\sin(5x^{2})\cos(6x^{2})dx
(dy)/(dx)=x^2+y	\frac{dy}{dx}=x^{2}+y
derivative of f(x)=x^3+2x^2+3x	derivative\:f(x)=x^{3}+2x^{2}+3x
integral of (x-1)/(x^2+2)	\int\:\frac{x-1}{x^{2}+2}dx
limit as x approaches 0 of ((7x^2-2x))/x	\lim\:_{x\to\:0}(\frac{(7x^{2}-2x)}{x})
laplacetransform 1-cos(2t)	laplacetransform\:1-\cos(2t)
roots xsin(y)	roots\:x\sin(y)
f^'(x)= x/8-1	f^{\prime\:}(x)=\frac{x}{8}-1
slope of y=2-x^3,P(1,1)	slope\:y=2-x^{3},P(1,1)
(\partial}{\partial x}(\frac{xe^x)/y)	\frac{\partial\:}{\partial\:x}(\frac{xe^{x}}{y})
implicit (dy)/(dx),e x/y =8x-y	implicit\:\frac{dy}{dx},e\frac{x}{y}=8x-y
25y^{'''}+40y^{''}+16y^'=0	25y^{\prime\:\prime\:\prime\:}+40y^{\prime\:\prime\:}+16y^{\prime\:}=0
derivative of 3arcsin(x^3)	\frac{d}{dx}(3\arcsin(x^{3}))
derivative of e^{2x}(2-x)	\frac{d}{dx}(e^{2x}(2-x))
integral of (3x^2-2)/(x^2-4x-12)	\int\:\frac{3x^{2}-2}{x^{2}-4x-12}dx
derivative of arcsin(x^{100})	\frac{d}{dx}(\arcsin(x^{100}))
inverse oflaplace (20)/(2x^2+9x+30)	inverselaplace\:\frac{20}{2x^{2}+9x+30}
laplacetransform e^{3t}sin(6t)	laplacetransform\:e^{3t}\sin(6t)
slope of y=sqrt(x)	slope\:y=\sqrt{x}
(\partial)/(\partial w)(xe^w)	\frac{\partial\:}{\partial\:w}(xe^{w})
derivative of (log_{2}(x))/x	derivative\:\frac{\log_{2}(x)}{x}
integral from 0 to 6 of xsqrt(36-x^2)	\int\:_{0}^{6}x\sqrt{36-x^{2}}dx
integral of-x^4ln(x)	\int\:-x^{4}\ln(x)dx
t^2y^{''}-ty^'+y=0	t^{2}y^{\prime\:\prime\:}-ty^{\prime\:}+y=0
(d^2)/(dx^2)((x^3)/(x^2-4))	\frac{d^{2}}{dx^{2}}(\frac{x^{3}}{x^{2}-4})
integral of cos(1)	\int\:\cos(1)dx
integral of (18x^3-36x^2+5)/(x^2-2x)	\int\:\frac{18x^{3}-36x^{2}+5}{x^{2}-2x}dx
(d^3)/(dx^3)(xe^x)	\frac{d^{3}}{dx^{3}}(xe^{x})
integral of x(3x+8)^5	\int\:x(3x+8)^{5}dx
integral of 4tan(x)sec^5(x)	\int\:4\tan(x)\sec^{5}(x)dx
derivative of-5x^4+4x^3-20x-20	\frac{d}{dx}(-5x^{4}+4x^{3}-20x-20)
sum from n=1 to infinity of cos((10)/n)	\sum\:_{n=1}^{\infty\:}\cos(\frac{10}{n})
tangent of y=x^2-6x,(5,-5)	tangent\:y=x^{2}-6x,(5,-5)
integral of (x^2-2)^3	\int\:(x^{2}-2)^{3}dx
integral of tan^3(x)cos(x)	\int\:\tan^{3}(x)\cos(x)dx
parity (tan^3(x))/(2x+1)	parity\:\frac{\tan^{3}(x)}{2x+1}
(\partial)/(\partial y)(xyzsqrt(x))	\frac{\partial\:}{\partial\:y}(xyz\sqrt{x})
maclaurin-ln(1-x^2)	maclaurin\:-\ln(1-x^{2})
derivative of x/(753600x^2+900)	\frac{d}{dx}(\frac{x}{753600x^{2}+900})
area y=4x+4,y=5x+5,x=2	area\:y=4x+4,y=5x+5,x=2
integral of (2x-1)/(x^2(x+3))	\int\:\frac{2x-1}{x^{2}(x+3)}dx
limit as x approaches 0 of ((2.7^x-1))/x	\lim\:_{x\to\:0}(\frac{(2.7^{x}-1)}{x})
d/(dt)(12t-40pisin(pit))	\frac{d}{dt}(12t-40π\sin(πt))
integral from 0 to 8pi of t^2sin(2t)	\int\:_{0}^{8π}t^{2}\sin(2t)dt
integral of ax+b	\int\:ax+bdx
integral of (e^x(x-1)-e^x)/((x-1)^2)	\int\:\frac{e^{x}(x-1)-e^{x}}{(x-1)^{2}}dx
derivative of tan(1/x)	derivative\:\tan(\frac{1}{x})
taylor 1/(2-x),1	taylor\:\frac{1}{2-x},1
derivative of (3x^3+x+2/(5x^2+1))	\frac{d}{dx}(\frac{3x^{3}+x+2}{5x^{2}+1})
(\partial)/(\partial x)(7ln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(7\ln(x^{2}+y^{2}))
sum from n=5 to infinity of 1/n	\sum\:_{n=5}^{\infty\:}\frac{1}{n}
x^{''}-5x^'+6x=e^t	x^{\prime\:\prime\:}-5x^{\prime\:}+6x=e^{t}
derivative of-7/(x^8)	\frac{d}{dx}(-\frac{7}{x^{8}})

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