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Popular Calculus Problems

sum from n=0 to infinity of (8n)/(6n+1)	\sum\:_{n=0}^{\infty\:}\frac{8n}{6n+1}
xy^{''}+2y^'=12x^2,y^'(1)=4,y(1)=0	xy^{\prime\:\prime\:}+2y^{\prime\:}=12x^{2},y^{\prime\:}(1)=4,y(1)=0
(x^2+(2y)/x)dx=(3-ln(x^2))dy	(x^{2}+\frac{2y}{x})dx=(3-\ln(x^{2}))dy
integral of 1+3sqrt(x)	\int\:1+3\sqrt{x}dx
integral of 28x^3-18x^2+10x	\int\:28x^{3}-18x^{2}+10xdx
derivative of 1/(x^{2/3})	\frac{d}{dx}(\frac{1}{x^{\frac{2}{3}}})
limit as x approaches 1 of arcsin(x)	\lim\:_{x\to\:1}(\arcsin(x))
derivative of (4x^2-5x+1/(3x+7))	\frac{d}{dx}(\frac{4x^{2}-5x+1}{3x+7})
integral from 1 to 4 of (5x^2+sqrt(x))	\int\:_{1}^{4}(5x^{2}+\sqrt{x})dx
csc(y)+sec^2(x)((dy)/(dx))=0	\csc(y)+\sec^{2}(x)(\frac{dy}{dx})=0
sum from n=1 to infinity of 3/(n(n+1))	\sum\:_{n=1}^{\infty\:}\frac{3}{n(n+1)}
area f(x)=x,g(x)=sqrt(x),x=0,2	area\:f(x)=x,g(x)=\sqrt{x},x=0,2
xy^'=8y-9x,y(1)=0,y(1)=0	xy^{\prime\:}=8y-9x,y(1)=0,y(1)=0
integral of x/(e^{6x)}	\int\:\frac{x}{e^{6x}}dx
area 3sqrt(x),(3x)/4	area\:3\sqrt{x},\frac{3x}{4}
derivative of (2x^5-5x^3+7x^4)	\frac{d}{dx}((2x^{5}-5x^{3}+7x)^{4})
integral from 1 to 4 of x^2+2x-5	\int\:_{1}^{4}x^{2}+2x-5dx
integral of (x-5)	\int\:(x-5)dx
area y=-3x+12,y=2x^2-11x+12	area\:y=-3x+12,y=2x^{2}-11x+12
integral of (sin(2s))/(cos(2s))	\int\:\frac{\sin(2s)}{\cos(2s)}ds
integral of 120x	\int\:120xdx
sum from n=1 to infinity of (n+1)/n	\sum\:_{n=1}^{\infty\:}\frac{n+1}{n}
limit as x approaches infinity+of (log_{4}(x))/(log_{7)(x)}	\lim\:_{x\to\:\infty\:+}(\frac{\log_{4}(x)}{\log_{7}(x)})
limit as x approaches 4 of sqrt(x^2+20)	\lim\:_{x\to\:4}(\sqrt{x^{2}+20})
derivative of (3x^2/(sqrt(x^2+2x-1)))	\frac{d}{dx}(\frac{3x^{2}}{\sqrt{x^{2}+2x-1}})
tangent of f(x)=x^3-3x+1,\at x=2	tangent\:f(x)=x^{3}-3x+1,\at\:x=2
integral of e^x-xe^x	\int\:e^{x}-xe^{x}dx
derivative of f(x)=-(42)/((x+4)^4)	derivative\:f(x)=-\frac{42}{(x+4)^{4}}
integral from 0 to 5 of 1/(x^{20/19)}	\int\:_{0}^{5}\frac{1}{x^{\frac{20}{19}}}dx
derivative of (x^2/(x^3+4))	\frac{d}{dx}(\frac{x^{2}}{x^{3}+4})
(\partial)/(\partial x)(5y-x+y^2sin(y))	\frac{\partial\:}{\partial\:x}(5y-x+y^{2}\sin(y))
(dy)/(dx)=y^3xe^{x^2}	\frac{dy}{dx}=y^{3}xe^{x^{2}}
y^{''}-8y=0	y^{\prime\:\prime\:}-8y=0
derivative of e^{x+y}	derivative\:e^{x+y}
integral from 1 to 4 of 5x+3x^2-8	\int\:_{1}^{4}5x+3x^{2}-8dx
(dy)/(dx)=-((2y^2))/(x^2)	\frac{dy}{dx}=-\frac{(2y^{2})}{x^{2}}
ax^{''}+bx=0	ax^{\prime\:\prime\:}+bx=0
derivative of e^{tanh(2x})	\frac{d}{dx}(e^{\tanh(2x)})
y^'-e^{2x+y}=0	y^{\prime\:}-e^{2x+y}=0
integral of 1-cos(6x)	\int\:1-\cos(6x)dx
limit as t approaches 1 of (1/t-1)/(t-1)	\lim\:_{t\to\:1}(\frac{\frac{1}{t}-1}{t-1})
sum from n=0 to infinity of n^2	\sum\:_{n=0}^{\infty\:}n^{2}
derivative of ln(x^2-y)	\frac{d}{dx}(\ln(x^{2}-y))
derivative of f(x)=(4x+5)(5x-6)	derivative\:f(x)=(4x+5)(5x-6)
slope ofintercept (0.5)(1.6)	slopeintercept\:(0.5)(1.6)
integral of x/(sqrt(x^2-25))	\int\:\frac{x}{\sqrt{x^{2}-25}}dx
(dy)/(dx)x^3+y^3=6xy	\frac{dy}{dx}x^{3}+y^{3}=6xy
limit as x approaches-3+of ((x+2))/(x+3)	\lim\:_{x\to\:-3+}(\frac{(x+2)}{x+3})
derivative of 9/(x^5)	\frac{d}{dx}(\frac{9}{x^{5}})
derivative of X	derivative\:X
integral of (sqrt(4x^2-1))/x	\int\:\frac{\sqrt{4x^{2}-1}}{x}dx
y^'=(x(x^2+1))/(4y^3),y(0)=-1/(sqrt(2))	y^{\prime\:}=\frac{x(x^{2}+1)}{4y^{3}},y(0)=-\frac{1}{\sqrt{2}}
inverse oflaplace ((s+1))/(s^2+s+3)	inverselaplace\:\frac{(s+1)}{s^{2}+s+3}
integral from 1 to 5 of 3	\int\:_{1}^{5}3dt
(\partial)/(\partial x)((a^2x^2+b^2y^2)^4)	\frac{\partial\:}{\partial\:x}((a^{2}x^{2}+b^{2}y^{2})^{4})
derivative of (ln(2))x	derivative\:(\ln(2))x
derivative of f(x)=sqrt(x^2-2x+1)	derivative\:f(x)=\sqrt{x^{2}-2x+1}
derivative of (x^3/3+c)	\frac{d}{dx}(\frac{x^{3}}{3}+c)
limit as x approaches 5 of (x^3+8)/(x+2)	\lim\:_{x\to\:5}(\frac{x^{3}+8}{x+2})
derivative of x-1/(1+x)	\frac{d}{dx}(x-\frac{1}{1+x})
integral of ((x+4))/(x^2+2x+5)	\int\:\frac{(x+4)}{x^{2}+2x+5}dx
inverse oflaplace s/((s^2+25)(s-1))	inverselaplace\:\frac{s}{(s^{2}+25)(s-1)}
x(x+1)(dy)/(dx)+xy=1,y(e)=1	x(x+1)\frac{dy}{dx}+xy=1,y(e)=1
((sqrt(x)+x)dy)/(dx)=sqrt(y)+y	\frac{(\sqrt{x}+x)dy}{dx}=\sqrt{y}+y
limit as x approaches 6+of x/(x-6)	\lim\:_{x\to\:6+}(\frac{x}{x-6})
taylor 1/(x^2)4	taylor\:\frac{1}{x^{2}}4
(\partial)/(\partial x)((6x-8y)/(6x+8y))	\frac{\partial\:}{\partial\:x}(\frac{6x-8y}{6x+8y})
(\partial)/(\partial y)((x^2+y^2)^{1/2})	\frac{\partial\:}{\partial\:y}((x^{2}+y^{2})^{\frac{1}{2}})
derivative of f(x)=x^2-4	derivative\:f(x)=x^{2}-4
integral of 1/(x^2(x+1)^2)	\int\:\frac{1}{x^{2}(x+1)^{2}}dx
derivative of sqrt(x)-2	derivative\:\sqrt{x}-2
tangent of 7x-4sqrt(x)	tangent\:7x-4\sqrt{x}
y^'-y^{5/3}=0	y^{\prime\:}-y^{\frac{5}{3}}=0
integral of x/(x-20)	\int\:\frac{x}{x-20}dx
maclaurin 1/(1+\frac{1){1+x}}	maclaurin\:\frac{1}{1+\frac{1}{1+x}}
derivative of 1/3 t^3-4t^2+16t+7	derivative\:\frac{1}{3}t^{3}-4t^{2}+16t+7
limit as x approaches 0 of log_{2}(x)	\lim\:_{x\to\:0}(\log_{2}(x))
integral of (x+6y)	\int\:(x+6y)dy
integral of (2sqrt(x))	\int\:(2\sqrt{x})dx
limit as x approaches 0 of 9^x	\lim\:_{x\to\:0}(9^{x})
inverse oflaplace s/(s^2+2s-3)	inverselaplace\:\frac{s}{s^{2}+2s-3}
integral of 11y	\int\:11ydy
f(x)=xcos(x)-sin(x)	f(x)=x\cos(x)-\sin(x)
derivative of ln(x^2sin(x))	\frac{d}{dx}(\ln(x^{2})\sin(x))
integral of ((y^2+1))/(y^2+4)	\int\:\frac{(y^{2}+1)}{y^{2}+4}dy
integral of (xsin(x))/((cos(x))^2)	\int\:\frac{x\sin(x)}{(\cos(x))^{2}}dx
inverse oflaplace 5/(4(s-3)^2-64)	inverselaplace\:\frac{5}{4(s-3)^{2}-64}
derivative of ln((x+2/(x^2)))	\frac{d}{dx}(\ln(\frac{x+2}{x^{2}}))
derivative of x^2y^4	\frac{d}{dx}(x^{2}y^{4})
limit as x approaches 2 of x^2-5	\lim\:_{x\to\:2}(x^{2}-5)
integral of 3x^2+cos(x)	\int\:3x^{2}+\cos(x)dx
limit as x approaches 0 of (1-e^{-x})/x	\lim\:_{x\to\:0}(\frac{1-e^{-x}}{x})
derivative of (x^2/(x^3))	\frac{d}{dx}(\frac{x^{2}}{x^{3}})
derivative of e^x(x^2+1)(x+4)	derivative\:e^{x}(x^{2}+1)(x+4)
taylor x^{1/3},1	taylor\:x^{\frac{1}{3}},1
area y=-x,y=-x^2+ex	area\:y=-x,y=-x^{2}+ex
parity (csc(3x))/(x^3)	parity\:\frac{\csc(3x)}{x^{3}}
derivative of f(x)=x^2+4x-4	derivative\:f(x)=x^{2}+4x-4
integral of 13x^{12}	\int\:13x^{12}dx
derivative of-(x-pi/2 tan(x))	\frac{d}{dx}(-(x-\frac{π}{2})\tan(x))

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