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Popular Calculus Problems

integral of sin(15/4)	\int\:\sin(\frac{15}{4})dθ
taylor ln(x/2)	taylor\:\ln(\frac{x}{2})
(dy)/(dx)(x+1)+y=ln(x),y(1)=10	\frac{dy}{dx}(x+1)+y=\ln(x),y(1)=10
area 2x^2,(3,18)	area\:2x^{2},(3,18)
x^2y^{''}+4xy^'+2y= 1/x	x^{2}y^{\prime\:\prime\:}+4xy^{\prime\:}+2y=\frac{1}{x}
3(dy)/(dx)+8/(xy^2)=0	3\frac{dy}{dx}+\frac{8}{xy^{2}}=0
derivative of 2/(x+5)	\frac{d}{dx}(\frac{2}{x+5})
limit as x approaches 0+of cot(x)-csc(x)	\lim\:_{x\to\:0+}(\cot(x)-\csc(x))
integral of sec(y)tan(y)	\int\:\sec(y)\tan(y)dy
derivative of 1/(x+7)	\frac{d}{dx}(\frac{1}{x+7})
integral of x^2sqrt(x+22)	\int\:x^{2}\sqrt{x+22}dx
limit as x approaches 0 of ax+b	\lim\:_{x\to\:0}(ax+b)
integral from 0 to 10 of e^xsin(x)	\int\:_{0}^{10}e^{x}\sin(x)dx
derivative of ((x^2+1/(x^2-1))^6)	\frac{d}{dx}((\frac{x^{2}+1}{x^{2}-1})^{6})
limit as x approaches 3-of x^2	\lim\:_{x\to\:3-}(x^{2})
integral from 0 to 1 of (x^3+4)/(x^2-25)	\int\:_{0}^{1}\frac{x^{3}+4}{x^{2}-25}dx
derivative of y=(9sqrt(x))/x	derivative\:y=\frac{9\sqrt{x}}{x}
integral of t*cos(nt)	\int\:t\cdot\:\cos(nt)dt
simplify x+y	simplify\:x+y
limit as x approaches 0 of ((sin(7x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(7x))}{x})
area x^3,3x+2	area\:x^{3},3x+2
(\partial)/(\partial y)(1/(xy^2z))	\frac{\partial\:}{\partial\:y}(\frac{1}{xy^{2}z})
integral of (x^2)ln(x)	\int\:(x^{2})\ln(x)dx
(e^{-y})^'	(e^{-y})^{\prime\:}
x(dy)/(dx)+xy^2=xy	x\frac{dy}{dx}+xy^{2}=xy
integral of (x-1)/(4x^3+4x^2+x)	\int\:\frac{x-1}{4x^{3}+4x^{2}+x}dx
integral of sin^2(2x+5)	\int\:\sin^{2}(2x+5)dx
(\partial)/(\partial x)(e^{-7y}cos(7x))	\frac{\partial\:}{\partial\:x}(e^{-7y}\cos(7x))
(dy)/(dx)= y/x+x/(2(y+x))	\frac{dy}{dx}=\frac{y}{x}+\frac{x}{2(y+x)}
integral from 0 to 1 of (2x+1)^3	\int\:_{0}^{1}(2x+1)^{3}dx
tangent of f(x)=sqrt(3x+7),(3,4)	tangent\:f(x)=\sqrt{3x+7},(3,4)
inverse oflaplace 1/(s(s^2+2s+2))	inverselaplace\:\frac{1}{s(s^{2}+2s+2)}
expand (x-2)^2(x+4)	expand\:(x-2)^{2}(x+4)
taylor x^{9/6},2	taylor\:x^{\frac{9}{6}},2
sum from n=0 to infinity of 1/(sin(n))	\sum\:_{n=0}^{\infty\:}\frac{1}{\sin(n)}
limit as x approaches pi/6 of xsin(x)	\lim\:_{x\to\:\frac{π}{6}}(x\sin(x))
y^'=3y	y^{\prime\:}=3y
tangent of y=x^2+2,(-3,11)	tangent\:y=x^{2}+2,(-3,11)
limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4)	\lim\:_{x\to\:1}(\frac{(\sqrt{26-x}-5)}{\sqrt{17-x}-4})
y^{''}-2y^'-3y=4e^{3t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=4e^{3t}
integral of-2e^{cos(x)}sin(x)	\int\:-2e^{\cos(x)}\sin(x)dx
derivative of f(x)=21	derivative\:f(x)=21
integral of cos^3(4x)sin^2(4x)	\int\:\cos^{3}(4x)\sin^{2}(4x)dx
(\partial)/(\partial x)(20arctan(x))	\frac{\partial\:}{\partial\:x}(20\arctan(x))
derivative of (4x^4-x+3)(-x^5+5)	derivative\:(4x^{4}-x+3)(-x^{5}+5)
(\partial)/(\partial x)(m/v)	\frac{\partial\:}{\partial\:x}(\frac{m}{v})
integral of e^{sin(a)}cos(a)	\int\:e^{\sin(a)}\cos(a)
area x=y^2-2,y=x	area\:x=y^{2}-2,y=x
integral of (5ln(x+8))/(x^2)	\int\:\frac{5\ln(x+8)}{x^{2}}dx
taylor sin(x)-x	taylor\:\sin(x)-x
y^{''}+4y=20sin(2t)	y^{\prime\:\prime\:}+4y=20\sin(2t)
tangent of f(x)=(5x)/(x+3),(2,2)	tangent\:f(x)=\frac{5x}{x+3},(2,2)
derivative of 13.375ln(x/(x-1250))	derivative\:13.375\ln(\frac{x}{x-1250})
integral of 6x(1-x)	\int\:6x(1-x)dx
t^2*y^'+ty=7,y(1)=7	t^{2}\cdot\:y^{\prime\:}+ty=7,y(1)=7
integral of 8sin^2(x)cos(x)	\int\:8\sin^{2}(x)\cos(x)dx
y^{''}+2y^'+y=3x+8	y^{\prime\:\prime\:}+2y^{\prime\:}+y=3x+8
derivative of acos(2x+bcos(2x))	\frac{d}{dx}(a\cos(2x)+b\cos(2x))
(\partial)/(\partial x)(y-5x)	\frac{\partial\:}{\partial\:x}(y-5x)
integral of x[2cos(x)-xsin(x)]	\int\:x[2\cos(x)-x\sin(x)]dx
limit as x approaches 2 of sqrt(6-3x)-3	\lim\:_{x\to\:2}(\sqrt{6-3x}-3)
integral of 1/(sqrt(1+9x^2))	\int\:\frac{1}{\sqrt{1+9x^{2}}}dx
integral of (8000ln(x+25))/((x+25)^2)	\int\:\frac{8000\ln(x+25)}{(x+25)^{2}}dx
(\partial)/(\partial y)(e^{-xyz})	\frac{\partial\:}{\partial\:y}(e^{-xyz})
derivative of-sqrt(x)	\frac{d}{dx}(-\sqrt{x})
tangent of (2+x)*e^x	tangent\:(2+x)\cdot\:e^{x}
2yy^'+2=y^2+2x,y(0)=9	2yy^{\prime\:}+2=y^{2}+2x,y(0)=9
integral of-5	\int\:-5dx
integral from 5 to 8 of (13-2x)	\int\:_{5}^{8}(13-2x)dx
area y=6+\sqrt[3]{x},x=0,x=8,y=0	area\:y=6+\sqrt[3]{x},x=0,x=8,y=0
derivative of 2x^2+3x	\frac{d}{dx}(2x^{2}+3x)
integral of (5/3)^x	\int\:(\frac{5}{3})^{x}dx
derivative of e^{-x}+1	\frac{d}{dx}(e^{-x}+1)
d/(dt)(1/(sqrt(t)))	\frac{d}{dt}(\frac{1}{\sqrt{t}})
integral of sec(x)(sec(x)-tan(x))	\int\:\sec(x)(\sec(x)-\tan(x))dx
integral from 0 to 1 of sqrt(1+(x)^2)	\int\:_{0}^{1}\sqrt{1+(x)^{2}}dx
tangent of (x-3)(x^2+6)	tangent\:(x-3)(x^{2}+6)
4x^3y+x^4y^'=-6sec^2(x)tan(x)	4x^{3}y+x^{4}y^{\prime\:}=-6\sec^{2}(x)\tan(x)
(\partial)/(\partial x)(Ae^{1/x})	\frac{\partial\:}{\partial\:x}(Ae^{\frac{1}{x}})
integral from 0 to 6 of 2pi(y+2)(3-y/2)	\int\:_{0}^{6}2π(y+2)(3-\frac{y}{2})dy
(dy)/(dx)-y/x =3xe^x	\frac{dy}{dx}-\frac{y}{x}=3xe^{x}
derivative of ln(xe^{-5x})	\frac{d}{dx}(\ln(xe^{-5x}))
integral from-2 to 2 of (1/((x+4)(x-4)))	\int\:_{-2}^{2}(\frac{1}{(x+4)(x-4)})dx
limit as x approaches 0-of csc(x)(x-1)	\lim\:_{x\to\:0-}(\csc(x)(x-1))
integral from-infinity to 0 of x^2e^x	\int\:_{-\infty\:}^{0}x^{2}e^{x}dx
(\partial)/(\partial x)((e^{xz+y})/(z^2+w))	\frac{\partial\:}{\partial\:x}(\frac{e^{xz+y}}{z^{2}+w})
derivative of 1/((x+9^2))	\frac{d}{dx}(\frac{1}{(x+9)^{2}})
(\partial)/(\partial x)((-x^4+7y^2+3y)^6)	\frac{\partial\:}{\partial\:x}((-x^{4}+7y^{2}+3y)^{6})
integral of 1+1/(2x)	\int\:1+\frac{1}{2x}dx
y^{''}-5y^'+4y=0,y(0)=3,y^'(0)=2	y^{\prime\:\prime\:}-5y^{\prime\:}+4y=0,y(0)=3,y^{\prime\:}(0)=2
integral from 1 to 3 of e^x	\int\:_{1}^{3}e^{x}dx
derivative of 18+(12)/((0.0004x^2+1)^2)	derivative\:18+\frac{12}{(0.0004x^{2}+1)^{2}}
integral from 3 to 6 of x/(x^2+6x+13)	\int\:_{3}^{6}\frac{x}{x^{2}+6x+13}dx
(\partial)/(\partial y)(2x^{4y})	\frac{\partial\:}{\partial\:y}(2x^{4y})
derivative of 9tan(x-9cot(x))	\frac{d}{dx}(9\tan(x)-9\cot(x))
derivative of x(17-2x(33-2x))	\frac{d}{dx}(x(17-2x)(33-2x))
limit as x approaches 0 of 2x^2+4x-2	\lim\:_{x\to\:0}(2x^{2}+4x-2)
12^'	12^{\prime\:}
limit as x approaches 1 of 2/(x^2-1)	\lim\:_{x\to\:1}(\frac{2}{x^{2}-1})
limit as x approaches-0 of f(x)	\lim\:_{x\to\:-0}(f(x))

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