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Popular Calculus Problems

integral from 2 to 5 of t^3ln(5t)	\int\:_{2}^{5}t^{3}\ln(5t)dt
derivative of (x-1(x-2)(2-x^2))	\frac{d}{dx}((x-1)(x-2)(2-x^{2}))
derivative of 3/(sqrt(6t+3))	derivative\:\frac{3}{\sqrt{6t+3}}
f^'(t)=(8t)/(8+sqrt(t))	f^{\prime\:}(t)=\frac{8t}{8+\sqrt{t}}
derivative of f(x)=(2x^2-1)^{1/2}	derivative\:f(x)=(2x^{2}-1)^{\frac{1}{2}}
y^{''}+8y^'+65y=0,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+8y^{\prime\:}+65y=0,y(0)=0,y^{\prime\:}(0)=0
limit as x approaches-2 of x^2-2x^2+2x+3	\lim\:_{x\to\:-2}(x^{2}-2x^{2}+2x+3)
derivative of (tan(x-1)/(sec(x)))	\frac{d}{dx}(\frac{\tan(x)-1}{\sec(x)})
integral of 8/(x^2-1)	\int\:\frac{8}{x^{2}-1}dx
integral of 7cos^3(x)	\int\:7\cos^{3}(x)dx
(\partial)/(\partial x)(8y^4x^7-7y^3x^6)	\frac{\partial\:}{\partial\:x}(8y^{4}x^{7}-7y^{3}x^{6})
implicit (dy)/(dx),y=x^2+4	implicit\:\frac{dy}{dx},y=x^{2}+4
d/(dt)(e^tsin(2t))	\frac{d}{dt}(e^{t}\sin(2t))
derivative of 2/((x-2^2))	\frac{d}{dx}(\frac{2}{(x-2)^{2}})
integral of (4x^3-x^2+2)/(x^4-x^3+x^2)	\int\:\frac{4x^{3}-x^{2}+2}{x^{4}-x^{3}+x^{2}}dx
4x^2(dy)/(dx)=(dy)/(dx)+4xe^{-y}	4x^{2}\frac{dy}{dx}=\frac{dy}{dx}+4xe^{-y}
integral from 0 to 1 of pi(y-y^4)	\int\:_{0}^{1}π(y-y^{4})dy
integral of (4x+6)/((x^2+3x+7)^3)	\int\:\frac{4x+6}{(x^{2}+3x+7)^{3}}dx
derivative of (sqrt(x^5))/8	derivative\:\frac{\sqrt{x^{5}}}{8}
inverse oflaplace (10)/s	inverselaplace\:\frac{10}{s}
limit as x approaches infinity of 1.02^x	\lim\:_{x\to\:\infty\:}(1.02^{x})
integral of 1/(sqrt(x^2+2x))	\int\:\frac{1}{\sqrt{x^{2}+2x}}dx
(\partial)/(\partial x)(x^2-kxe^{3y}-3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-kxe^{3y}-3y^{2})
tangent of f(x)=x^2-5,(2,-1)	tangent\:f(x)=x^{2}-5,(2,-1)
tangent of ((5x-4))/(x-1)	tangent\:\frac{(5x-4)}{x-1}
derivative of-st	\frac{d}{dx}(-st)
integral of 1/(x^2sqrt(x))	\int\:\frac{1}{x^{2}\sqrt{x}}dx
derivative of 3ln(x)	derivative\:3\ln(x)
integral of 1/(x(x+1)^2)	\int\:\frac{1}{x(x+1)^{2}}dx
derivative of e^{-2x}*cos(3x)	\frac{d}{dx}(e^{-2x}\cdot\:\cos(3x))
limit as x approaches 0+of 3+x^5ln(x)	\lim\:_{x\to\:0+}(3+x^{5}\ln(x))
(\partial)/(\partial y)(x^3+yz^2)	\frac{\partial\:}{\partial\:y}(x^{3}+yz^{2})
integral of 1/(sqrt(x-2))	\int\:\frac{1}{\sqrt{x-2}}dx
derivative of csc(cot(x))	\frac{d}{dx}(\csc(\cot(x)))
limit as x approaches 1+of (x+2)/(x-1)	\lim\:_{x\to\:1+}(\frac{x+2}{x-1})
(\partial)/(\partial y)(sqrt(x^2+y^2-2))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}+y^{2}-2})
integral of (3x-x^{-1})^2	\int\:(3x-x^{-1})^{2}dx
derivative of x/(sqrt(x^2+a^2))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+a^{2}}})
integral of 1/(e^{3y)}	\int\:\frac{1}{e^{3y}}dy
f(r)=2pir^2	f(r)=2πr^{2}
derivative of (8x+7(x^2-3x))	\frac{d}{dx}((8x+7)(x^{2}-3x))
derivative of sin(2pi(1-x))	\frac{d}{dx}(\sin(2π(1-x)))
integral of (cos(t))/(7+sin(t))	\int\:\frac{\cos(t)}{7+\sin(t)}dt
area y=x^2+10x+25,y=7x+35	area\:y=x^{2}+10x+25,y=7x+35
integral of 1/((1+x)(1-x))	\int\:\frac{1}{(1+x)(1-x)}dx
derivative of 1/(x-9)	derivative\:\frac{1}{x-9}
derivative of (1-6x/(5+x))	\frac{d}{dx}(\frac{1-6x}{5+x})
integral of 1/(8-x)	\int\:\frac{1}{8-x}dx
derivative of 7x+8	\frac{d}{dx}(7x+8)
taylor ze^z	taylor\:ze^{z}
limit as x approaches 2 of \sqrt[3]{x}	\lim\:_{x\to\:2}(\sqrt[3]{x})
sum from n=0 to infinity of (n/(n+3))^n	\sum\:_{n=0}^{\infty\:}(\frac{n}{n+3})^{n}
limit as x approaches 1 of 4x-2	\lim\:_{x\to\:1}(4x-2)
derivative of 2sin(x)cos(x)	derivative\:2\sin(x)\cos(x)
(dy)/(dx)=y,y(7)=8	\frac{dy}{dx}=y,y(7)=8
(\partial)/(\partial y)(sin(3x)cos(3y))	\frac{\partial\:}{\partial\:y}(\sin(3x)\cos(3y))
derivative of ((e^{b/x}))/((e^{b/x)-1)}	derivative\:\frac{(e^{\frac{b}{x}})}{(e^{\frac{b}{x}}-1)}
derivative of (x^2sin(x)^5)	\frac{d}{dx}((x^{2}\sin(x))^{5})
integral of (e^x)/(x+1)	\int\:\frac{e^{x}}{x+1}dx
d/(dt)((sec^2(t))/(sec(t)tan(t)))	\frac{d}{dt}(\frac{\sec^{2}(t)}{\sec(t)\tan(t)})
integral from-2 to 1 of 1/(x^4)	\int\:_{-2}^{1}\frac{1}{x^{4}}dx
(\partial)/(\partial x)(2y^2+3x)	\frac{\partial\:}{\partial\:x}(2y^{2}+3x)
integral of (x^{10})/(x^2+x-2)	\int\:\frac{x^{10}}{x^{2}+x-2}dx
integral of (x^2)/((x^3-2)^3)	\int\:\frac{x^{2}}{(x^{3}-2)^{3}}dx
derivative of (8x^2+4x+8/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+4x+8}{\sqrt{x}})
tangent of 4x^3,\at x=1	tangent\:4x^{3},\at\:x=1
tangent of f(x)=sqrt(5-3x),\at x= 1/3	tangent\:f(x)=\sqrt{5-3x},\at\:x=\frac{1}{3}
derivative of tan(x)	derivative\:\tan(x)
derivative of f(x)= 5/(r^3)	derivative\:f(x)=\frac{5}{r^{3}}
inverse oflaplace (20)/(s(s^2+4s+4))	inverselaplace\:\frac{20}{s(s^{2}+4s+4)}
limit as x approaches infinity of (sqrt(7x^3+8x))/(4x-3)	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{7x^{3}+8x}}{4x-3})
integral of (W/U)	\int\:(\frac{W}{U})dW
derivative of 2x-x^3	\frac{d}{dx}(2x-x^{3})
d/(d{x)}({x}^2+{y}^2+{z}^2+{x}{y})	\frac{d}{d{x}}({x}^{2}+{y}^{2}+{z}^{2}+{x}{y})
xy^2+3y^2-x^2y^'=0	xy^{2}+3y^{2}-x^{2}y^{\prime\:}=0
derivative of (3x-2/(2x-3))	\frac{d}{dx}(\frac{3x-2}{2x-3})
integral of 1/(t^{3/2)}	\int\:\frac{1}{t^{\frac{3}{2}}}dt
integral of 2/(1+4x^2)	\int\:\frac{2}{1+4x^{2}}dx
integral of sin(1/2)	\int\:\sin(\frac{1}{2})
derivative of z^3	derivative\:z^{3}
(\partial)/(\partial x)(-x^2y^2z+2xy^2z^2)	\frac{\partial\:}{\partial\:x}(-x^{2}y^{2}z+2xy^{2}z^{2})
derivative of (x+y^{1/2})	\frac{d}{dx}((x+y)^{\frac{1}{2}})
integral of 5xarctan(x)	\int\:5x\arctan(x)dx
(\partial)/(\partial y)((e^x-4x)cos(y))	\frac{\partial\:}{\partial\:y}((e^{x}-4x)\cos(y))
integral of 1/x+(y^2)/(x^2)	\int\:\frac{1}{x}+\frac{y^{2}}{x^{2}}dx
derivative of ln((x-1^3(x^2+1)^4))	\frac{d}{dx}(\ln((x-1)^{3}(x^{2}+1)^{4}))
derivative of 3x^2-e^{2x}	\frac{d}{dx}(3x^{2}-e^{2x})
(dy}{dt}=-\frac{3y)/t-2-t^{-4}	\frac{dy}{dt}=-\frac{3y}{t}-2-t^{-4}
(\partial)/(\partial z)(cos(xy)+sin(yz))	\frac{\partial\:}{\partial\:z}(\cos(xy)+\sin(yz))
integral of sin^3(x)cos^2(x)	\int\:\sin^{3}(x)\cos^{2}(x)dx
integral from 1 to e^2 of (ln^5(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{5}(x^{2})}{x}dx
derivative of f(x)=(4x-5)(3x^3-x^2+1)	derivative\:f(x)=(4x-5)(3x^{3}-x^{2}+1)
integral of (x-3)/(x^2-1)	\int\:\frac{x-3}{x^{2}-1}dx
derivative of sqrt(x^3)	derivative\:\sqrt{x^{3}}
integral of (2x^2+1)/x	\int\:\frac{2x^{2}+1}{x}dx
limit as x approaches 1 of (x^4-1)/(x^2)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x^{2}})
derivative of f(x)=(2x^2-4)^{-1}	derivative\:f(x)=(2x^{2}-4)^{-1}
limit as x approaches 8-of x/(x^2-64)	\lim\:_{x\to\:8-}(\frac{x}{x^{2}-64})
derivative of (-2x^2+9/(sqrt(9-x^2)))	\frac{d}{dx}(\frac{-2x^{2}+9}{\sqrt{9-x^{2}}})
y^'=(y+2t)^2,y(0)=sqrt(3)	y^{\prime\:}=(y+2t)^{2},y(0)=\sqrt{3}

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