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Popular Calculus Problems

1+y^2+2(t+1)y(dy)/(dt)=0,y(0)=1	1+y^{2}+2(t+1)y\frac{dy}{dt}=0,y(0)=1
x(dy)/(dx)+(1-3x)y=e^{5x}	x\frac{dy}{dx}+(1-3x)y=e^{5x}
f(x)=(sin(x))/(e^x)	f(x)=\frac{\sin(x)}{e^{x}}
integral of (x^3+1.8x^2-2.4x)	\int\:(x^{3}+1.8x^{2}-2.4x)dx
(\partial)/(\partial y)(2y-x)	\frac{\partial\:}{\partial\:y}(2y-x)
integral of x^2(5+2x^3)^8	\int\:x^{2}(5+2x^{3})^{8}dx
e^{x+2y}dx-e^{2x-y}dy=0	e^{x+2y}dx-e^{2x-y}dy=0
sum from n=5 to infinity of (sin(n))/(n^{3/2)}	\sum\:_{n=5}^{\infty\:}\frac{\sin(n)}{n^{\frac{3}{2}}}
integral of 5/(x^5)	\int\:\frac{5}{x^{5}}dx
integral of 2e^{cos(x)}sin(x)	\int\:2e^{\cos(x)}\sin(x)dx
integral of (3x-1/x-7e^x+14e)	\int\:(3x-\frac{1}{x}-7e^{x}+14e)dx
integral of (5sec^2(x))/(2(1-tan(x)))	\int\:\frac{5\sec^{2}(x)}{2(1-\tan(x))}dx
derivative of xy+1	\frac{d}{dx}(xy+1)
derivative of 3(sin(2xcos(x)-sin^3(x)))	\frac{d}{dx}(3(\sin(2x)\cos(x)-\sin^{3}(x)))
integral from 0 to 3 of xsqrt(x^2+1)	\int\:_{0}^{3}x\sqrt{x^{2}+1}dx
integral of 1/(20-y)	\int\:\frac{1}{20-y}dy
derivative of sin(ln(x)+cos(ln(x)))	\frac{d}{dx}(\sin(\ln(x))+\cos(\ln(x)))
derivative of f(x)=-3x^3	derivative\:f(x)=-3x^{3}
inverse oflaplace ((s+6))/((s^2+6s+25))	inverselaplace\:\frac{(s+6)}{(s^{2}+6s+25)}
derivative of sqrt(x)+4/(sqrt(x))	\frac{d}{dx}(\sqrt{x}+\frac{4}{\sqrt{x}})
integral of (x+1)^2ln(x+1)	\int\:(x+1)^{2}\ln(x+1)dx
y^'=y^4	y^{\prime\:}=y^{4}
derivative of 5^{xsin(x})	\frac{d}{dx}(5^{x\sin(x)})
tangent of f(x)=2x^3,\at x=1	tangent\:f(x)=2x^{3},\at\:x=1
d/(dt)(1/(1+24e^{-0.28t)})	\frac{d}{dt}(\frac{1}{1+24e^{-0.28t}})
xy^'+2y=3x,y(1)=5	xy^{\prime\:}+2y=3x,y(1)=5
integral of x/((x^2+2)^{4/3)}	\int\:\frac{x}{(x^{2}+2)^{\frac{4}{3}}}dx
y^'=3y-y^2	y^{\prime\:}=3y-y^{2}
derivative of csqrt(x)	derivative\:c\sqrt{x}
y^'-4/x y=(y^3)/(x^3),y(1)=1	y^{\prime\:}-\frac{4}{x}y=\frac{y^{3}}{x^{3}},y(1)=1
derivative of 7/10 x^2+4x^3	\frac{d}{dx}(\frac{7}{10}x^{2}+4x^{3})
(dy)/(dx)-y=-x/2	\frac{dy}{dx}-y=-\frac{x}{2}
limit as x approaches 0 of 1-1/(x^2)	\lim\:_{x\to\:0}(1-\frac{1}{x^{2}})
limit as x approaches 3 of ((x^2-2x-3))/(x^2-9)	\lim\:_{x\to\:3}(\frac{(x^{2}-2x-3)}{x^{2}-9})
y^'(x^2+2)+4x(y^2+2y+1)=0	y^{\prime\:}(x^{2}+2)+4x(y^{2}+2y+1)=0
derivative of (1+cos(5t))^{-4}	derivative\:(1+\cos(5t))^{-4}
derivative of (x^2+2/x)	\frac{d}{dx}(\frac{x^{2}+2}{x})
integral of (-5e^{-5x})/((e^{-5x)+3)^3}	\int\:\frac{-5e^{-5x}}{(e^{-5x}+3)^{3}}dx
limit as s approaches 2-of s+\|3s-6\|	\lim\:_{s\to\:2-}(s+\left\|3s-6\right\|)
derivative of (sin(x+cos(x))/(sin(x)))	\frac{d}{dx}(\frac{\sin(x)+\cos(x)}{\sin(x)})
join (ax^2)/(ln(x/4))+(bx^4)/(x-4)	join\:\frac{ax^{2}}{\ln(\frac{x}{4})}+\frac{bx^{4}}{x-4}
(\partial)/(\partial x)(3x^2y^2-1)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{2}-1)
maclaurin sqrt(x^2-1)	maclaurin\:\sqrt{x^{2}-1}
sum from n=2 to infinity of 1/(n(n+1))	\sum\:_{n=2}^{\infty\:}\frac{1}{n(n+1)}
integral of x^{(-2)/3}sqrt(x^{1/3)-2}	\int\:x^{\frac{-2}{3}}\sqrt{x^{\frac{1}{3}}-2}dx
integral of ()/(s^2(s-1)^2)	\int\:\frac{ds}{s^{2}(s-1)^{2}}dx
derivative of 2/(sqrt(x)-(sqrt(3x))/3)	\frac{d}{dx}(\frac{2}{\sqrt{x}}-\frac{\sqrt{3x}}{3})
derivative of (x^3/4+1/(3x))	\frac{d}{dx}(\frac{x^{3}}{4}+\frac{1}{3x})
integral of 2	\int\:2dx
limit as x approaches 1 of [5f(x)+g(x)]	\lim\:_{x\to\:1}([5f(x)+g(x)])
derivative of ln(ex)	\frac{d}{dx}(\ln(ex))
integral of (2x)/(x^2sqrt(x^4-1))	\int\:\frac{2x}{x^{2}\sqrt{x^{4}-1}}dx
partialfraction (x^2)/(x^2+4)	partialfraction\:\frac{x^{2}}{x^{2}+4}
limit as x approaches 4 of 2/((x-4)^4)	\lim\:_{x\to\:4}(\frac{2}{(x-4)^{4}})
integral of (e^{3x}+1/x)	\int\:(e^{3x}+\frac{1}{x})dx
limit as x approaches 0 of (2^{3x}-1)/x	\lim\:_{x\to\:0}(\frac{2^{3x}-1}{x})
integral of sin^2(θ)	\int\:\sin^{2}(θ)dθ
integral of ln((x+1)/(x-1))	\int\:\ln(\frac{x+1}{x-1})dx
integral of 7/(xsqrt(49-(ln(x))^2))	\int\:\frac{7}{x\sqrt{49-(\ln(x))^{2}}}dx
derivative of 2x^3-e^x	\frac{d}{dx}(2x^{3}-e^{x})
integral of sin^3(x)cos^5(x)	\int\:\sin^{3}(x)\cos^{5}(x)dx
limit as x approaches infinity of e^{2x}	\lim\:_{x\to\:\infty\:}(e^{2x})
derivative of (2x/(1-2x))	\frac{d}{dx}(\frac{2x}{1-2x})
integral of arcsin(6x)	\int\:\arcsin(6x)dx
slope of (3,1),(0,-2)	slope\:(3,1),(0,-2)
derivative of 5*2^{sqrt(t-2)}	derivative\:5\cdot\:2^{\sqrt{t-2}}
sum from n=4 to infinity of e^{7-4n}	\sum\:_{n=4}^{\infty\:}e^{7-4n}
limit as x approaches infinity of \sqrt[4]{n}*(sqrt(n+3))/(2n+1)	\lim\:_{x\to\:\infty\:}(\sqrt[4]{n}\cdot\:\frac{\sqrt{n+3}}{2n+1})
integral of 4\sqrt[3]{16-4x}-8	\int\:4\sqrt[3]{16-4x}-8dx
(\partial)/(\partial x)(sin(x)*cos(x))	\frac{\partial\:}{\partial\:x}(\sin(x)\cdot\:\cos(x))
limit as x approaches+(-1) of x+2x^4	\lim\:_{x\to\:+(-1)}(x+2x^{4})
tangent of-1/((x-5)^2)	tangent\:-\frac{1}{(x-5)^{2}}
derivative of e^{x^0}	\frac{d}{dx}(e^{x^{0}})
integral from 1 to 3 of x/((2x-1)^3)	\int\:_{1}^{3}\frac{x}{(2x-1)^{3}}dx
integral of xln(sqrt(5)x)	\int\:x\ln(\sqrt{5}x)dx
integral of 1/(sqrt(x)(\sqrt{x+1))}	\int\:\frac{1}{\sqrt{x}(\sqrt{x+1})}dx
integral of 1/((x^2+81)^{3/2)}	\int\:\frac{1}{(x^{2}+81)^{\frac{3}{2}}}dx
limit as x approaches 8 of ((x^2-5x-24))/(x-8)	\lim\:_{x\to\:8}(\frac{(x^{2}-5x-24)}{x-8})
integral of (sqrt(x)+sqrt(a))^2	\int\:(\sqrt{x}+\sqrt{a})^{2}dx
derivative of 7+cot(x)-2csc(x)	derivative\:7+\cot(x)-2\csc(x)
(dy)/(dx)=-3-2x-y	\frac{dy}{dx}=-3-2x-y
integral of 1/(sqrt(-x^2+8x-12))	\int\:\frac{1}{\sqrt{-x^{2}+8x-12}}dx
derivative of-(In(x^3)/x)	\frac{d}{dx}(-\frac{In(x^{3})}{x})
implicit x^5+x^2y+9y^2=13	implicit\:x^{5}+x^{2}y+9y^{2}=13
area y=4x-x^2,y=3-x	area\:y=4x-x^{2},y=3-x
(\partial)/(\partial x)(cos(3x))	\frac{\partial\:}{\partial\:x}(\cos(3x))
integral of (sec(x)-1/(sin(x))+cos(x))	\int\:(\sec(x)-\frac{1}{\sin(x)}+\cos(x))dx
(\partial)/(\partial x)(sin(x/(1+y)))	\frac{\partial\:}{\partial\:x}(\sin(\frac{x}{1+y}))
integral of (x^2)/(\sqrt[3]{x+3)}	\int\:\frac{x^{2}}{\sqrt[3]{x+3}}dx
integral of 27sec^{-2}(xta)n^3x	\int\:27\sec^{-2}(xta)n^{3}xdx
(dy)/(dx)=y(c_{1}+pi^2)(1+x)^{-1}	\frac{dy}{dx}=y(c_{1}+π^{2})(1+x)^{-1}
derivative of sqrt(1-cos(x))	\frac{d}{dx}(\sqrt{1-\cos(x)})
integral of sin(9t)sin(4t)	\int\:\sin(9t)\sin(4t)dt
derivative of 2xtan(2x+2)	\frac{d}{dx}(2x\tan(2x+2))
sqrt(y)y^'+y^{3/2}=1	\sqrt{y}y^{\prime\:}+y^{\frac{3}{2}}=1
(\partial)/(\partial x)(ln(x^7-y^6))	\frac{\partial\:}{\partial\:x}(\ln(x^{7}-y^{6}))
integral of 5tan^2(x)sec(x)	\int\:5\tan^{2}(x)\sec(x)dx
integral of arctan(1)	\int\:\arctan(1)dx
derivative of (pi-xcos(x))	\frac{d}{dx}((π-x)\cos(x))
derivative of 2x^2-4x-1	derivative\:2x^{2}-4x-1

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