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Popular Calculus Problems

sum from n=5 to infinity of 3(0.9)^{n+1}	\sum\:_{n=5}^{\infty\:}3(0.9)^{n+1}
limit as x approaches 0 of x-ln(x)	\lim\:_{x\to\:0}(x-\ln(x))
y^'+y^5x+9y=0	y^{\prime\:}+y^{5}x+9y=0
limit as x approaches-pi/2 of tan(x)	\lim\:_{x\to\:-\frac{π}{2}}(\tan(x))
derivative of sqrt(x)+\sqrt[5]{x}	derivative\:\sqrt{x}+\sqrt[5]{x}
integral of 1/(2e^{2x)}	\int\:\frac{1}{2e^{2x}}dx
integral from 0 to 1 of pi(x-x^3)^2	\int\:_{0}^{1}π(x-x^{3})^{2}dx
tangent of 2x^3-6x^2-18-3	tangent\:2x^{3}-6x^{2}-18-3
area y=-2x^2+6,y=-2	area\:y=-2x^{2}+6,y=-2
integral of 1/(sin^2(x)\sqrt[4]{cot(x))}	\int\:\frac{1}{\sin^{2}(x)\sqrt[4]{\cot(x)}}dx
integral of sqrt(1+x^2)*x^5	\int\:\sqrt{1+x^{2}}\cdot\:x^{5}dx
tangent of y=-x^3+2x^2-4,\at x=-1	tangent\:y=-x^{3}+2x^{2}-4,\at\:x=-1
derivative of-sec^2(x)	derivative\:-\sec^{2}(x)
d/(dn)(e^{nipi})	\frac{d}{dn}(e^{niπ})
y^{''}+y^'+y=0	y^{\prime\:\prime\:}+y^{\prime\:}+y=0
integral of (y^5+5y)	\int\:(y^{5}+5y)dy
y^{''}+y=0,y(pi/3)=16,y^'(pi/3)=-32	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=16,y^{\prime\:}(\frac{π}{3})=-32
(\partial)/(\partial y)(7e^{x^2ln(y)})	\frac{\partial\:}{\partial\:y}(7e^{x^{2}\ln(y)})
derivative of 5Y^{5/8}X^{3/8}	derivative\:5Y^{\frac{5}{8}}X^{\frac{3}{8}}
integral of 1/(3x+12)	\int\:\frac{1}{3x+12}dx
(\partial)/(\partial y)(e^{x+y+4})	\frac{\partial\:}{\partial\:y}(e^{x+y+4})
(dy)/(dx)=3y+1	\frac{dy}{dx}=3y+1
derivative of 2+cos(2x)	\frac{d}{dx}(2+\cos(2x))
taylor xsin(x)	taylor\:x\sin(x)
tangent of y=(1+4x)^{3/2}	tangent\:y=(1+4x)^{\frac{3}{2}}
integral of (5sqrt(x+25))/x	\int\:\frac{5\sqrt{x+25}}{x}dx
laplacetransform 3e^t(32t^2+2t+15)	laplacetransform\:3e^{t}(32t^{2}+2t+15)
integral of 3/(e^q+2)	\int\:\frac{3}{e^{q}+2}dq
integral of e^{R/L t}	\int\:e^{\frac{R}{L}t}dt
derivative of f(x)=4x-3x+7	derivative\:f(x)=4x-3x+7
integral of 1/(x^2+2x+101)	\int\:\frac{1}{x^{2}+2x+101}dx
integral of 2/(sqrt(2-x^2))	\int\:\frac{2}{\sqrt{2-x^{2}}}dx
derivative of ln(\sqrt[4]{x})	derivative\:\ln(\sqrt[4]{x})
(\partial)/(\partial x)({f}(x,y))	\frac{\partial\:}{\partial\:x}({f}(x,y))
derivative of (3x/2)	\frac{d}{dx}(\frac{3x}{2})
tangent of sqrt(x-2)	tangent\:\sqrt{x-2}
y^{''}-12y^'+54y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+54y=0
derivative of f(θ)=θcos(θ)	derivative\:f(θ)=θ\cos(θ)
sum from n=2 to infinity of 1/(n^2)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}}
derivative of y=x^{-4}	derivative\:y=x^{-4}
integral of x^3-5x	\int\:x^{3}-5xdx
implicit e^{xy}+y=x-1	implicit\:e^{xy}+y=x-1
simplify x/(sqrt(x^2+4))	simplify\:\frac{x}{\sqrt{x^{2}+4}}
(\partial)/(\partial x)(3e^{x-y})	\frac{\partial\:}{\partial\:x}(3e^{x-y})
integral from 6 to 8 of (52)/((x-6)^3)	\int\:_{6}^{8}\frac{52}{(x-6)^{3}}dx
integral of (18x)/(sqrt(1-9x^2))	\int\:\frac{18x}{\sqrt{1-9x^{2}}}dx
integral of 3x(6-x^2)	\int\:3x(6-x^{2})dx
integral of (-1)^nx^n	\int\:(-1)^{n}x^{n}dx
integral of y^3(2y^2-3)	\int\:y^{3}(2y^{2}-3)dy
(\partial)/(\partial x)(2y+ye^x)	\frac{\partial\:}{\partial\:x}(2y+ye^{x})
(dx)/(dt)=-3x	\frac{dx}{dt}=-3x
limit as h approaches 0 of (e^{2h}-1)/h	\lim\:_{h\to\:0}(\frac{e^{2h}-1}{h})
derivative of sqrt(x)*cos(x)	\frac{d}{dx}(\sqrt{x}\cdot\:\cos(x))
tangent of f(x)=2xsqrt(5-2x),\at x=-1	tangent\:f(x)=2x\sqrt{5-2x},\at\:x=-1
integral of r	\int\:rdr
y^'=1+y^2	y^{\prime\:}=1+y^{2}
derivative of f(x)=3x^2-x+3	derivative\:f(x)=3x^{2}-x+3
derivative of (x-17/(sqrt(x)-\sqrt{17)})	\frac{d}{dx}(\frac{x-17}{\sqrt{x}-\sqrt{17}})
integral of sqrt(4-x^2)(16-4x^2)	\int\:\sqrt{4-x^{2}}(16-4x^{2})dx
integral of cos(xz)	\int\:\cos(xz)dx
(dy)/(dx)=0.0012y(2300-y)	\frac{dy}{dx}=0.0012y(2300-y)
integral of (x-5)^2	\int\:(x-5)^{2}dx
integral from 1 to 3 of x^3ln(x)	\int\:_{1}^{3}x^{3}\ln(x)dx
derivative of (3x/(2x+1))	\frac{d}{dx}(\frac{3x}{2x+1})
integral of (6x+5)/(6x^2)	\int\:\frac{6x+5}{6x^{2}}dx
sum from n=1 to infinity of-1/n	\sum\:_{n=1}^{\infty\:}-\frac{1}{n}
derivative of x*ln^2(x)	\frac{d}{dx}(x\cdot\:\ln^{2}(x))
integral of 4cos(x)+9sin(x)	\int\:4\cos(x)+9\sin(x)dx
integral of 5/((3x+5)^4)	\int\:\frac{5}{(3x+5)^{4}}dx
derivative of f(x)=sqrt((4x+1)/(2x^2+1))	derivative\:f(x)=\sqrt{\frac{4x+1}{2x^{2}+1}}
integral of (x-y)/(x+y)	\int\:\frac{x-y}{x+y}dy
integral of 9x^{1/2}	\int\:9x^{\frac{1}{2}}dx
derivative of 2x^2+6	\frac{d}{dx}(2x^{2}+6)
limit as x approaches infinity of 2x-3	\lim\:_{x\to\:\infty\:}(2x-3)
taylor 5/(sqrt(x)),4	taylor\:\frac{5}{\sqrt{x}},4
sum from n=0 to infinity of 1/(e^{5n)}	\sum\:_{n=0}^{\infty\:}\frac{1}{e^{5n}}
integral of (-4x^3+2e^{-2x}+1/(2x))	\int\:(-4x^{3}+2e^{-2x}+\frac{1}{2x})dx
(dy)/(dx)+4(tan(4x))y=10cos(4x)	\frac{dy}{dx}+4(\tan(4x))y=10\cos(4x)
limit as x approaches 0 of x/((4^x-2^x))	\lim\:_{x\to\:0}(\frac{x}{(4^{x}-2^{x})})
derivative of arcsin(2x^5)	\frac{d}{dx}(\arcsin(2x^{5}))
tangent of sqrt(x^2+9)	tangent\:\sqrt{x^{2}+9}
derivative of (5x^3+5(x^4-3x))	\frac{d}{dx}((5x^{3}+5)(x^{4}-3x))
integral of [cos(4x)+cos(8x)]^2	\int\:[\cos(4x)+\cos(8x)]^{2}dx
derivative of 12x^{1/3}	\frac{d}{dx}(12x^{\frac{1}{3}})
(dy)/(dx)= 1/(3x^2y^2)	\frac{dy}{dx}=\frac{1}{3x^{2}y^{2}}
(4pir^2)^'	(4πr^{2})^{\prime\:}
derivative of (x-1^2(x-2)(x-4))	\frac{d}{dx}((x-1)^{2}(x-2)(x-4))
tangent of y=(2x)/((x^2+1))	tangent\:y=\frac{2x}{(x^{2}+1)}
integral of 8/((4x^2+1)^2)	\int\:\frac{8}{(4x^{2}+1)^{2}}dx
integral of (6-72x)/(sqrt(1-36x^2))	\int\:\frac{6-72x}{\sqrt{1-36x^{2}}}dx
derivative of (sqrt(x)/(x+2))	\frac{d}{dx}(\frac{\sqrt{x}}{x+2})
derivative of (x+4/(x-5))	\frac{d}{dx}(\frac{x+4}{x-5})
derivative of sqrt(23x)	derivative\:\sqrt{23x}
derivative of (x^2+2x/(4x))	\frac{d}{dx}(\frac{x^{2}+2x}{4x})
integral from 1 to 2 of 1/(x^8)	\int\:_{1}^{2}\frac{1}{x^{8}}dx
sum from n=1 to infinity of 2/((n+2)^3)	\sum\:_{n=1}^{\infty\:}\frac{2}{(n+2)^{3}}
derivative of e^{3x-3}	\frac{d}{dx}(e^{3x-3})
derivative of y=5x^2cos^2(y)	\frac{d}{dx}y=5x^{2}\cos^{2}(y)
tangent of f(x)=2xcos(x),\at x=(3pi)/2	tangent\:f(x)=2x\cos(x),\at\:x=\frac{3π}{2}
integral of 2sin^3(xco)s^5x	\int\:2\sin^{3}(xco)s^{5}xdx

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