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Popular Calculus Problems

inverse oflaplace (e^{-4s})/(s^2+4s+3)	inverselaplace\:\frac{e^{-4s}}{s^{2}+4s+3}
derivative of-2x+3	derivative\:-2x+3
y^'=(x-y)/2	y^{\prime\:}=\frac{x-y}{2}
area y=17-x^2,y=-2x+14	area\:y=17-x^{2},y=-2x+14
integral of 1/(x^2+2x-15)	\int\:\frac{1}{x^{2}+2x-15}dx
4y^{''}-4y^'-3y=cos(2t)	4y^{\prime\:\prime\:}-4y^{\prime\:}-3y=\cos(2t)
inverse oflaplace (s^2)/s	inverselaplace\:\frac{s^{2}}{s}
integral of 5+cot^2(x)	\int\:5+\cot^{2}(x)dx
integral of sec^6(x)tan^4(x)	\int\:\sec^{6}(x)\tan^{4}(x)dx
integral of-x^{-1}	\int\:-x^{-1}dx
integral of (1+1/x)^3(1/(x^2))	\int\:(1+\frac{1}{x})^{3}(\frac{1}{x^{2}})dx
limit as x approaches pi/6 of sin(2x-pi)	\lim\:_{x\to\:\frac{π}{6}}(\sin(2x-π))
d/(dt)(e^t(acos(2t)+bsin(2t)))	\frac{d}{dt}(e^{t}(a\cos(2t)+b\sin(2t)))
integral of (sqrt(x))/(x^3)	\int\:\frac{\sqrt{x}}{x^{3}}dx
integral from 2 to 3 of (24)/(sqrt(3-x))	\int\:_{2}^{3}\frac{24}{\sqrt{3-x}}dx
derivative of f(x)= 5/(ln(x))	derivative\:f(x)=\frac{5}{\ln(x)}
integral of (sin(1/(x^2)))/(x^3)	\int\:\frac{\sin(\frac{1}{x^{2}})}{x^{3}}dx
integral of ((x+3))/(sqrt(x^2+4))	\int\:\frac{(x+3)}{\sqrt{x^{2}+4}}dx
integral of 1/(x(1+x))	\int\:\frac{1}{x(1+x)}dx
integral of (5e^{5t})/(7+e^{5t)}	\int\:\frac{5e^{5t}}{7+e^{5t}}dt
(\partial)/(\partial x)(3x+2ysin(x))	\frac{\partial\:}{\partial\:x}(3x+2y\sin(x))
derivative of 6^xlog_{3}(x)	\frac{d}{dx}(6^{x}\log_{3}(x))
derivative of y=(6x^2-10x+1)^{-4}	derivative\:y=(6x^{2}-10x+1)^{-4}
integral of [((sin(sqrt(x))))/(sqrt(x))]	\int\:[\frac{(\sin(\sqrt{x}))}{\sqrt{x}}]dx
(dy)/(dx)+xy=4x	\frac{dy}{dx}+xy=4x
(\partial)/(\partial y)(25-x^2-y^2)	\frac{\partial\:}{\partial\:y}(25-x^{2}-y^{2})
derivative of arctan(8x)	\frac{d}{dx}(\arctan(8x))
derivative of y=(9x)^{3x}	derivative\:y=(9x)^{3x}
integral of 1/(x(x-5)^2)	\int\:\frac{1}{x(x-5)^{2}}dx
derivative of ln(1/x+1/(x^2))	\frac{d}{dx}(\ln(\frac{1}{x}+\frac{1}{x^{2}}))
integral of (3x-5)/(x^2(x+5))	\int\:\frac{3x-5}{x^{2}(x+5)}dx
integral of (2x-1)(3x+4)	\int\:(2x-1)(3x+4)dx
integral of 0.002	\int\:0.002dx
y^{''}-4y^'=16t,y(0)=4,y^'(0)=0	y^{\prime\:\prime\:}-4y^{\prime\:}=16t,y(0)=4,y^{\prime\:}(0)=0
tangent of 1-2x-3x^2	tangent\:1-2x-3x^{2}
x(dy)/(dx)=x^3+11x^3y	x\frac{dy}{dx}=x^{3}+11x^{3}y
derivative of (tan(x)-1)/(sec(x))	derivative\:\frac{\tan(x)-1}{\sec(x)}
yy^'=1	yy^{\prime\:}=1
integral of (e^{sqrt(3x)})/(sqrt(3x))	\int\:\frac{e^{\sqrt{3x}}}{\sqrt{3x}}dx
limit as t approaches 0 of t*ln(t)	\lim\:_{t\to\:0}(t\cdot\:\ln(t))
limit as y approaches 1 of (y^4-1)/(y-1)	\lim\:_{y\to\:1}(\frac{y^{4}-1}{y-1})
derivative of (2x^3-7)/(x^2)	derivative\:\frac{2x^{3}-7}{x^{2}}
xy^'=y-x	xy^{\prime\:}=y-x
derivative of (5x^3+2^4)	\frac{d}{dx}((5x^{3}+2)^{4})
derivative of 6/(x^2-9)	\frac{d}{dx}(\frac{6}{x^{2}-9})
tangent of f(x)=sqrt(7x+4),\at x=3	tangent\:f(x)=\sqrt{7x+4},\at\:x=3
derivative of (x^5+9/(x^3))	\frac{d}{dx}(\frac{x^{5}+9}{x^{3}})
integral of 1/((x^2+a^2))	\int\:\frac{1}{(x^{2}+a^{2})}dx
area y=sin(x),y=cos(x),x=0,x=2pi	area\:y=\sin(x),y=\cos(x),x=0,x=2π
derivative of e^{x^6}+log_{5}(pi)	\frac{d}{dx}(e^{x^{6}}+\log_{5}(π))
(\partial)/(\partial x)(2x+3y-6)	\frac{\partial\:}{\partial\:x}(2x+3y-6)
derivative of (9-x^3)^{-2}	derivative\:(9-x^{3})^{-2}
derivative of 1/4 x^4-2x^3+9/2 x^2+1	\frac{d}{dx}(\frac{1}{4}x^{4}-2x^{3}+\frac{9}{2}x^{2}+1)
integral from 0 to 3 of 1/(x^2+3)	\int\:_{0}^{3}\frac{1}{x^{2}+3}dx
tangent of 1-x-x^2	tangent\:1-x-x^{2}
integral of tan^3(x)sec^9(x)	\int\:\tan^{3}(x)\sec^{9}(x)dx
integral of x^2(x+1)^3	\int\:x^{2}(x+1)^{3}dx
(3y^2+2xy)-(2xy+x^2)(dy)/(dx)=0	(3y^{2}+2xy)-(2xy+x^{2})\frac{dy}{dx}=0
derivative of sqrt(3)(s^3-s^2)	derivative\:\sqrt{3}(s^{3}-s^{2})
derivative of f(r)= 6/(r^3)	derivative\:f(r)=\frac{6}{r^{3}}
limit as x approaches 2pi of x*csc(x)	\lim\:_{x\to\:2π}(x\cdot\:\csc(x))
area x^2-12,x-6	area\:x^{2}-12,x-6
integral from 0 to 1 of x+y	\int\:_{0}^{1}x+ydy
integral from 3 to 6 of (x-4)^2	\int\:_{3}^{6}(x-4)^{2}dx
integral of sqrt(1-(x^2)/4)	\int\:\sqrt{1-\frac{x^{2}}{4}}dx
integral of (2^t+e^pi)	\int\:(2^{t}+e^{π})dt
y^'=e^{4x}(cos(x)+sin(x))	y^{\prime\:}=e^{4x}(\cos(x)+\sin(x))
(\partial)/(\partial z)((x^2-y^2)/(z^2))	\frac{\partial\:}{\partial\:z}(\frac{x^{2}-y^{2}}{z^{2}})
derivative of ((6-sec(x))/(tan(x)))	\frac{d}{dx}(\frac{(6-\sec(x))}{\tan(x)})
sum from n=1 to infinity of (3/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{3}{2})^{n}
integral of (6x+4)/(3x^2+4x+5)	\int\:\frac{6x+4}{3x^{2}+4x+5}dx
area x^3-1,x=-1,x=2	area\:x^{3}-1,x=-1,x=2
integral from-10 to 10 of 1/(100+x^2)	\int\:_{-10}^{10}\frac{1}{100+x^{2}}dx
integral of (x+sqrt(x))	\int\:(x+\sqrt{x})dx
derivative of 3(x^2+5x)^3	derivative\:3(x^{2}+5x)^{3}
derivative of 6x*sin(3x^2)	\frac{d}{dx}(6x\cdot\:\sin(3x^{2}))
derivative of ln((4-x/(4+x)))	\frac{d}{dx}(\ln(\frac{4-x}{4+x}))
integral from 0 to 3 of c(3-x)	\int\:_{0}^{3}c(3-x)dx
integral of (5x-3)/(x+1)	\int\:\frac{5x-3}{x+1}dx
derivative of f(x)= 4/(3x^2)	derivative\:f(x)=\frac{4}{3x^{2}}
integral of (x^2e^x)/((x+2)^2)	\int\:\frac{x^{2}e^{x}}{(x+2)^{2}}dx
integral of-(18)/(x^{19)}	\int\:-\frac{18}{x^{19}}dx
(dx)/(dt)-x/(t-1)=t^2+2	\frac{dx}{dt}-\frac{x}{t-1}=t^{2}+2
limit as x approaches 0 of ((1+x)^2-1)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{2}-1}{x})
y^'=1+9x-5y	y^{\prime\:}=1+9x-5y
integral of (cos(x))/(sin^4(x))	\int\:\frac{\cos(x)}{\sin^{4}(x)}dx
implicit y^2=x^2(x+1)	implicit\:y^{2}=x^{2}(x+1)
derivative of (6x)/(x^2+1)	derivative\:\frac{6x}{x^{2}+1}
(\partial)/(\partial y)(ye^x+sin(y))	\frac{\partial\:}{\partial\:y}(ye^{x}+\sin(y))
derivative of-7sin(7x)	derivative\:-7\sin(7x)
sum from n=1 to infinity of n/((n+1))	\sum\:_{n=1}^{\infty\:}\frac{n}{(n+1)}
derivative of e^{-x^2}-2e^{-x^2}x^2	\frac{d}{dx}(e^{-x^{2}}-2e^{-x^{2}}x^{2})
x^2y^'=xy+y^2	x^{2}y^{\prime\:}=xy+y^{2}
integral of x(x+4)^7	\int\:x(x+4)^{7}dx
integral of (10sin(2x))/(1+cos^4(x))	\int\:\frac{10\sin(2x)}{1+\cos^{4}(x)}dx
(dy)/(dx)y=ln(2)(x+3)	\frac{dy}{dx}y=\ln(2)(x+3)
integral of (x+8)/(2x^3-18x)	\int\:\frac{x+8}{2x^{3}-18x}dx
integral of ln(4)	\int\:\ln(4)
y^{''}-6y^'+9y=0,y(0)=3,y^'(0)= 25/3	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=0,y(0)=3,y^{\prime\:}(0)=\frac{25}{3}
derivative of (x^4/4 ln(x)-(x^4)/(16))	\frac{d}{dx}(\frac{x^{4}}{4}\ln(x)-\frac{x^{4}}{16})

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