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Popular Calculus Problems

laplacetransform e^{-2x}	laplacetransform\:e^{-2x}
(1-x)y^'-4xy^'+5y=cos(x)	(1-x)y^{\prime\:}-4xy^{\prime\:}+5y=\cos(x)
derivative of (1-x/(e^x))	\frac{d}{dx}(\frac{1-x}{e^{x}})
(\partial)/(\partial x)(-ycos(-3x))	\frac{\partial\:}{\partial\:x}(-y\cos(-3x))
sum from n=2 to infinity of ((n-1))/n	\sum\:_{n=2}^{\infty\:}\frac{(n-1)}{n}
derivative of-x^4+2x^3+4x^2	derivative\:-x^{4}+2x^{3}+4x^{2}
f(x)=3x^2+2	f(x)=3x^{2}+2
integral of 2^{ln(x)}	\int\:2^{\ln(x)}dx
derivative of f(x)=sqrt(x-2)	derivative\:f(x)=\sqrt{x-2}
integral from 0 to L of sin^2((pix)/L)	\int\:_{0}^{L}\sin^{2}(\frac{πx}{L})dx
derivative of (3/5 x^3)	\frac{d}{dx}((\frac{3}{5}x)^{3})
derivative of f(x)=sqrt(2x+1)	derivative\:f(x)=\sqrt{2x+1}
sum from n=0 to infinity of 1/(nsqrt(n))	\sum\:_{n=0}^{\infty\:}\frac{1}{n\sqrt{n}}
integral of 1/(1+sin(x)-cos(x))	\int\:\frac{1}{1+\sin(x)-\cos(x)}dx
integral from 0 to pi/2 of cos^3(x)	\int\:_{0}^{\frac{π}{2}}\cos^{3}(x)dx
derivative of sin(x-3)	\frac{d}{dx}(\sin(x-3))
limit as x approaches 2 of (3x)/(x^2+2)	\lim\:_{x\to\:2}(\frac{3x}{x^{2}+2})
(\partial)/(\partial y)(2x^4y+1)	\frac{\partial\:}{\partial\:y}(2x^{4}y+1)
area y=4x-x^2,y=3x	area\:y=4x-x^{2},y=3x
sum from n=4 to infinity of 4/(n^2-1)	\sum\:_{n=4}^{\infty\:}\frac{4}{n^{2}-1}
derivative of 7/(3x-1)	derivative\:\frac{7}{3x-1}
inverse oflaplace (10)/(s^3)	inverselaplace\:\frac{10}{s^{3}}
limit as x approaches infinity of x^2+12	\lim\:_{x\to\:\infty\:}(x^{2}+12)
derivative of (pix/4)	\frac{d}{dx}(\frac{πx}{4})
laplacetransform 45(1-e^{-625x})	laplacetransform\:45(1-e^{-625x})
tangent of f(x)= 1/(1+x^2),(2, 2/5)	tangent\:f(x)=\frac{1}{1+x^{2}},(2,\frac{2}{5})
derivative of x^2(3x-4^3)	\frac{d}{dx}(x^{2}(3x-4)^{3})
integral from 0 to 1 of x^2e^x	\int\:_{0}^{1}x^{2}e^{x}dx
area y=(16)/(x^2-6x-55),y=0,x=-3,x=3	area\:y=\frac{16}{x^{2}-6x-55},y=0,x=-3,x=3
derivative of t^5-1/(\sqrt[4]{t^7)}	derivative\:t^{5}-\frac{1}{\sqrt[4]{t^{7}}}
derivative of (x^3/((1-x)^2))	\frac{d}{dx}(\frac{x^{3}}{(1-x)^{2}})
d/(d{x)}({x}^2+{y}^2-{z})	\frac{d}{d{x}}({x}^{2}+{y}^{2}-{z})
integral of x^r	\int\:x^{r}dx
derivative of (x^2-6x+12)/(x-4)	derivative\:\frac{x^{2}-6x+12}{x-4}
y^'+y=e^{-x}sqrt(x)	y^{\prime\:}+y=e^{-x}\sqrt{x}
integral of (2x^2+7x+2)/((x^2+1)^2)	\int\:\frac{2x^{2}+7x+2}{(x^{2}+1)^{2}}dx
derivative of 3x^{2/3}-x	\frac{d}{dx}(3x^{\frac{2}{3}}-x)
derivative of (2x+1^{-1})	\frac{d}{dx}((2x+1)^{-1})
integral of (arcsin(sqrt(x)))/(sqrt(x))	\int\:\frac{\arcsin(\sqrt{x})}{\sqrt{x}}dx
y^{''}+16y^'+80y=0	y^{\prime\:\prime\:}+16y^{\prime\:}+80y=0
derivative of-x^3+3x^2+9x-1	\frac{d}{dx}(-x^{3}+3x^{2}+9x-1)
taylor e^{2x},-2	taylor\:e^{2x},-2
integral of 1/(-x^2+249x+250)	\int\:\frac{1}{-x^{2}+249x+250}dx
limit as x approaches infinity of ((ln(3x)))/(e^{7x)}	\lim\:_{x\to\:\infty\:}(\frac{(\ln(3x))}{e^{7x}})
sum from n=0 to infinity of (-5)^n	\sum\:_{n=0}^{\infty\:}(-5)^{n}
integral from 0 to 1 of (1+4xy)	\int\:_{0}^{1}(1+4xy)dx
tangent of y=3+4x^2-2x^3,(2,3)	tangent\:y=3+4x^{2}-2x^{3},(2,3)
derivative of (4+csc(x)/(8-csc(x)))	\frac{d}{dx}(\frac{4+\csc(x)}{8-\csc(x)})
integral of 4x^3ln(x)	\int\:4x^{3}\ln(x)dx
derivative of cx+ln(cos(x))	\frac{d}{dx}(cx+\ln(\cos(x)))
y^'+ry^{''}=0	y^{\prime\:}+ry^{\prime\:\prime\:}=0
derivative of (x^2+2^{-5}(cos(x)))	\frac{d}{dx}((x^{2}+2)^{-5}(\cos(x)))
integral from 1200 to 1210 of 0.1x^2	\int\:_{1200}^{1210}0.1x^{2}dx
derivative of ((x^2+1)/(x^2-1))^7	derivative\:(\frac{x^{2}+1}{x^{2}-1})^{7}
derivative of (x^3-3x(2x^2+3x+5))	\frac{d}{dx}((x^{3}-3x)(2x^{2}+3x+5))
sum from n=0 to infinity of 1/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{3^{n}}
f(x)=\sqrt[7]{ln(x)}	f(x)=\sqrt[7]{\ln(x)}
integral of (15)/(25+x^2)	\int\:\frac{15}{25+x^{2}}dx
limit as x approaches-2 of 2/(x+2)	\lim\:_{x\to\:-2}(\frac{2}{x+2})
(dy)/(dt)-2y=e^{2t}	\frac{dy}{dt}-2y=e^{2t}
integral of x^5(x^6-10)^4	\int\:x^{5}(x^{6}-10)^{4}dx
(x^2+4)dy=(2x-8y)dx	(x^{2}+4)dy=(2x-8y)dx
limit as n approaches 6 of (-1)^n7n	\lim\:_{n\to\:6}((-1)^{n}7n)
limit as x approaches 3 of-x^2+9x-8	\lim\:_{x\to\:3}(-x^{2}+9x-8)
derivative of f(x)=dcos(t)+t^2sin(t)	derivative\:f(x)=d\cos(t)+t^{2}\sin(t)
d/(dt)(1+4sqrt(t))	\frac{d}{dt}(1+4\sqrt{t})
y^{''}-2y^'+5y=0,y(pi/2)=0,y^'(pi/2)=2	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=0,y(\frac{π}{2})=0,y^{\prime\:}(\frac{π}{2})=2
limit as x approaches 0 of (ln(x))-1/x	\lim\:_{x\to\:0}((\ln(x))-\frac{1}{x})
limit as x approaches-2 of-(x^2-x+1)	\lim\:_{x\to\:-2}(-(x^{2}-x+1))
integral from 1 to 2 of x^{10}	\int\:_{1}^{2}x^{10}dx
derivative of y= 5/(x^2)	derivative\:y=\frac{5}{x^{2}}
derivative of ln(e^{7x-2})	derivative\:\ln(e^{7x-2})
y^{''}+4y^'+10y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+10y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of 1/(2+cos(x))	\frac{d}{dx}(\frac{1}{2+\cos(x)})
d/(dy)(e^yy^e)	\frac{d}{dy}(e^{y}y^{e})
integral of 4e^xcos(2x)	\int\:4e^{x}\cos(2x)dx
tangent of f(x)=(1+3x)(5-2x),\at x=2	tangent\:f(x)=(1+3x)(5-2x),\at\:x=2
inverse oflaplace s/((s+1)(s^2+4))	inverselaplace\:\frac{s}{(s+1)(s^{2}+4)}
(d^2)/(dx^2)(1/(x^{10)})	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{10}})
integral of-tan(t)	\int\:-\tan(t)dt
inverse oflaplace 3/((s+1)^2+1)	inverselaplace\:\frac{3}{(s+1)^{2}+1}
(\partial)/(\partial x)(y/x-1)	\frac{\partial\:}{\partial\:x}(\frac{y}{x}-1)
derivative of f(x)=cos((x^2-25)/(x-5))	derivative\:f(x)=\cos(\frac{x^{2}-25}{x-5})
limit as x approaches 0 of (2x+x^2)/x	\lim\:_{x\to\:0}(\frac{2x+x^{2}}{x})
integral of 4x^3nxx	\int\:4x^{3}nxxdx
(dy)/(dx)=(y^2-x^2)/(2xy)	\frac{dy}{dx}=\frac{y^{2}-x^{2}}{2xy}
inverse oflaplace (s^4+1)/(s^3-s)	inverselaplace\:\frac{s^{4}+1}{s^{3}-s}
integral of sin(8x)cos(4x)	\int\:\sin(8x)\cos(4x)dx
tangent of f(x)=(4x)/(x-3),\at x=5	tangent\:f(x)=\frac{4x}{x-3},\at\:x=5
derivative of (10/9)t^2	derivative\:(\frac{10}{9})t^{2}
5y^{''}+y^'=-6x	5y^{\prime\:\prime\:}+y^{\prime\:}=-6x
(\partial)/(\partial x)(y-3x)	\frac{\partial\:}{\partial\:x}(y-3x)
limit as x approaches 0 of x/(sin(pix))	\lim\:_{x\to\:0}(\frac{x}{\sin(πx)})
limit as x approaches-infinity of x^5	\lim\:_{x\to\:-\infty\:}(x^{5})
limit as x approaches 1 of 3x^2+2x+1	\lim\:_{x\to\:1}(3x^{2}+2x+1)
derivative of xcos(1/x)	\frac{d}{dx}(x\cos(\frac{1}{x}))
integral of (2x+21)/(2x^2+9x-5)	\int\:\frac{2x+21}{2x^{2}+9x-5}dx
limit as x approaches-1 of (x+2x^3)^4	\lim\:_{x\to\:-1}((x+2x^{3})^{4})
integral of (x^5)/(sqrt(1-2x^2))	\int\:\frac{x^{5}}{\sqrt{1-2x^{2}}}dx
integral of sqrt(1+4r^2)r	\int\:\sqrt{1+4r^{2}}rdr

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