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Popular Calculus Problems

inverse oflaplace s/((s^2+25)^2)	inverselaplace\:\frac{s}{(s^{2}+25)^{2}}
integral of 3x(5-x)	\int\:3x(5-x)dx
limit as x approaches 0 of x/(2tan(x))	\lim\:_{x\to\:0}(\frac{x}{2\tan(x)})
derivative of (x^3/6)	\frac{d}{dx}(\frac{x^{3}}{6})
integral from 0 to 1 of 1/(5x-3)	\int\:_{0}^{1}\frac{1}{5x-3}dx
2y^{''}+y^'-y=x+1	2y^{\prime\:\prime\:}+y^{\prime\:}-y=x+1
limit as x approaches 3 of x^2+4x-3	\lim\:_{x\to\:3}(x^{2}+4x-3)
derivative of x^3-4	\frac{d}{dx}(x^{3}-4)
integral of (1-x)^5(x+1)^2	\int\:(1-x)^{5}(x+1)^{2}dx
f(x)=sqrt(x^2+3)	f(x)=\sqrt{x^{2}+3}
integral of (cos(x)+sec(x))^2	\int\:(\cos(x)+\sec(x))^{2}dx
integral of (4x^2+3+5/(x^2+1))	\int\:(4x^{2}+3+\frac{5}{x^{2}+1})dx
integral from 3 to 4 of 5x	\int\:_{3}^{4}5xdx
y^{''}+9y=18	y^{\prime\:\prime\:}+9y=18
sum from n=1 to infinity of (15n!)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{15n!}{n^{n}}
(\partial)/(\partial x)(2x+3y+6xye^{3x^2y})	\frac{\partial\:}{\partial\:x}(2x+3y+6xye^{3x^{2}y})
(\partial)/(\partial x)(x^2+xe^{2y})	\frac{\partial\:}{\partial\:x}(x^{2}+xe^{2y})
derivative of (2arctan(x)/(1+x^2))	\frac{d}{dx}(\frac{2\arctan(x)}{1+x^{2}})
area x=0,y=x^2,y=x+2	area\:x=0,y=x^{2},y=x+2
limit as x approaches-1 of-6	\lim\:_{x\to\:-1}(-6)
derivative of sqrt(9x-(sin^2(2x)))	derivative\:\sqrt{9x-(\sin^{2}(2x))}
(\partial)/(\partial x)(xsin(y))	\frac{\partial\:}{\partial\:x}(x\sin(y))
area x^2,8-x^2,4x+12	area\:x^{2},8-x^{2},4x+12
derivative of 7^{x^2-x}	derivative\:7^{x^{2}-x}
integral from 0 to pi/2 of cos^4(2x)	\int\:_{0}^{\frac{π}{2}}\cos^{4}(2x)dx
x(dy)/(dx)-y=2x^2y^2	x\frac{dy}{dx}-y=2x^{2}y^{2}
derivative of sin(2)x^3	derivative\:\sin(2)x^{3}
limit as x approaches 2+of sqrt(x-2)	\lim\:_{x\to\:2+}(\sqrt{x-2})
f(x)=arccsc(x)	f(x)=\arccsc(x)
tangent of f(x)=ln(tan(2x)),\at x= pi/8	tangent\:f(x)=\ln(\tan(2x)),\at\:x=\frac{π}{8}
derivative of (e^x+1/(e^{2x)-5e^x+6})	\frac{d}{dx}(\frac{e^{x}+1}{e^{2x}-5e^{x}+6})
(\partial)/(\partial x)(2x+3x^2y)	\frac{\partial\:}{\partial\:x}(2x+3x^{2}y)
(xe^{-3x})^'	(xe^{-3x})^{\prime\:}
integral from 0 to 2 of x^3-3x^2+4	\int\:_{0}^{2}x^{3}-3x^{2}+4dx
y^'-(5y)/x =3x^4,y(1)=5	y^{\prime\:}-\frac{5y}{x}=3x^{4},y(1)=5
2sqrt(x)(dy)/(dx)=(cos^2(y))	2\sqrt{x}\frac{dy}{dx}=(\cos^{2}(y))
limit as x approaches 0+of 5/(1+x)	\lim\:_{x\to\:0+}(\frac{5}{1+x})
derivative of (3sqrt(z)-sin(z))/(-e^z)	derivative\:\frac{3\sqrt{z}-\sin(z)}{-e^{z}}
integral of 2e^xsqrt(9+e^x)	\int\:2e^{x}\sqrt{9+e^{x}}dx
integral of (-5sec^2(x))	\int\:(-5\sec^{2}(x))dx
integral from-2 to-1 of x^{-3}	\int\:_{-2}^{-1}x^{-3}dx
limit as x approaches 1 of (1-1/x)/(1-x)	\lim\:_{x\to\:1}(\frac{1-\frac{1}{x}}{1-x})
integral from 0 to pi of sec^2(t/3)	\int\:_{0}^{π}\sec^{2}(\frac{t}{3})dt
derivative of f(x)= 3/(\sqrt[3]{x)}	derivative\:f(x)=\frac{3}{\sqrt[3]{x}}
tangent of y=x^3,(-2,-8)	tangent\:y=x^{3},(-2,-8)
sum from n=1 to infinity of ((-3)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(-3)^{n}}{n}
derivative of x-x^{-1}	\frac{d}{dx}(x-x^{-1})
y^'-3/x y=(y^4)/(x^2)	y^{\prime\:}-\frac{3}{x}y=\frac{y^{4}}{x^{2}}
d/(ds)(si)	\frac{d}{ds}(si)
derivative of (x^2+1)/(sqrt(x))	derivative\:\frac{x^{2}+1}{\sqrt{x}}
integral of sin(x)cos(n)x	\int\:\sin(x)\cos(n)xdx
y^'= t/(1+t^2)*e^y	y^{\prime\:}=\frac{t}{1+t^{2}}\cdot\:e^{y}
limit as n approaches infinity of x/n	\lim\:_{n\to\:\infty\:}(\frac{x}{n})
d/(d{r)}(1/({r)^2})	\frac{d}{d{r}}(\frac{1}{{r}^{2}})
derivative of 1/3 x^{-2/3}	derivative\:\frac{1}{3}x^{-\frac{2}{3}}
integral of sin^3(v)cos^8(v)	\int\:\sin^{3}(v)\cos^{8}(v)dv
d/(dn)((n+1)^n)	\frac{d}{dn}((n+1)^{n})
derivative of f(x)=(sin(5x))/(3x)	derivative\:f(x)=\frac{\sin(5x)}{3x}
derivative of 7/(1-x)	derivative\:\frac{7}{1-x}
derivative of (12/((1-x)^5))	\frac{d}{dx}(\frac{12}{(1-x)^{5}})
sum from n=3 to infinity of (x^n)/(n!)	\sum\:_{n=3}^{\infty\:}\frac{x^{n}}{n!}
integral of 1/(sqrt(1-49x^2))	\int\:\frac{1}{\sqrt{1-49x^{2}}}dx
integral of (x^2-25)/(x-5)	\int\:\frac{x^{2}-25}{x-5}dx
(\partial)/(\partial y)(4x^3y^3)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3})
area y=2x^2-1,(0,1)	area\:y=2x^{2}-1,(0,1)
limit as x approaches 4 of 4x^2+5x+1	\lim\:_{x\to\:4}(4x^{2}+5x+1)
derivative of 3x+3	\frac{d}{dx}(3x+3)
limit as x approaches 0 of x/(sin(x/4))	\lim\:_{x\to\:0}(\frac{x}{\sin(\frac{x}{4})})
derivative of e^x-2-x	\frac{d}{dx}(e^{x}-2-x)
y^'-9/x y=(y^4)/(x^{13)},y(1)=1	y^{\prime\:}-\frac{9}{x}y=\frac{y^{4}}{x^{13}},y(1)=1
(dx)/(dt)-4x=cos(3t),x(0)=-1	\frac{dx}{dt}-4x=\cos(3t),x(0)=-1
derivative of 7e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(7e^{x}+\frac{2}{\sqrt[3]{x}})
limit as x approaches-2 of (x^2+5x)^2	\lim\:_{x\to\:-2}((x^{2}+5x)^{2})
limit as t approaches pi of-8sin(t/2)	\lim\:_{t\to\:π}(-8\sin(\frac{t}{2}))
(\partial)/(\partial y)(x^ay^b)	\frac{\partial\:}{\partial\:y}(x^{a}y^{b})
integral from 0 to pi of sec^2(x)	\int\:_{0}^{π}\sec^{2}(x)dx
derivative of cy^{-4}	derivative\:cy^{-4}
integral of (3x^{1/3})	\int\:(3x^{\frac{1}{3}})dx
integral of (e^{3x+9}-3x^2)	\int\:(e^{3x+9}-3x^{2})dx
derivative of y=8arcsin(x/4)-(xsqrt(16-x^2))/2	derivative\:y=8\arcsin(\frac{x}{4})-\frac{x\sqrt{16-x^{2}}}{2}
(\partial)/(\partial x)(e^ycos(x))	\frac{\partial\:}{\partial\:x}(e^{y}\cos(x))
integral from-1 to 1 of 9x^2+6x-3	\int\:_{-1}^{1}9x^{2}+6x-3dx
(\partial)/(\partial x)(3x^2-3y)	\frac{\partial\:}{\partial\:x}(3x^{2}-3y)
derivative of 1/(1+x+x^2)	\frac{d}{dx}(\frac{1}{1+x+x^{2}})
(-x^2)^'	(-x^{2})^{\prime\:}
derivative of xe^{x+1}	\frac{d}{dx}(xe^{x+1})
(2+x)(dy)/(dx)=3y	(2+x)\frac{dy}{dx}=3y
integral from 0 to 2 of 2t^3	\int\:_{0}^{2}2t^{3}dt
derivative of sqrt(x)+sqrt(y)=2	\frac{d}{dx}(\sqrt{x}+\sqrt{y})=2
derivative of sqrt(8t^2+9)	derivative\:\sqrt{8t^{2}+9}
integral of x^2e^{1x}	\int\:x^{2}e^{1x}dx
integral of (e^x+e^{2x})/(e^x)	\int\:\frac{e^{x}+e^{2x}}{e^{x}}dx
laplacetransform e^{-2t}sin(t)	laplacetransform\:e^{-2t}\sin(t)
limit as x approaches a of 3/0	\lim\:_{x\to\:a}(\frac{3}{0})
inverse oflaplace (20)/(s(s+10))	inverselaplace\:\frac{20}{s(s+10)}
derivative of (-x^2-4)/((x^2-4)^2)	derivative\:\frac{-x^{2}-4}{(x^{2}-4)^{2}}
sum from n=0 to infinity of 1/((1+n^2))	\sum\:_{n=0}^{\infty\:}\frac{1}{(1+n^{2})}
derivative of t^{-2}	derivative\:t^{-2}
sum from n=0 to infinity of 1/(7^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{7^{n}}
(dy}{dx}=\frac{(x+sec^2(x)))/y	\frac{dy}{dx}=\frac{(x+\sec^{2}(x))}{y}

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