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Popular Calculus Problems

integral of ((x^2+1))/(sqrt(x^3+3x))	\int\:\frac{(x^{2}+1)}{\sqrt{x^{3}+3x}}dx
(\partial)/(\partial x)(ln(x^6+y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{6}+y^{4}))
derivative of sqrt(5+4x)	derivative\:\sqrt{5+4x}
derivative of f(x)=(4x)/((x-1)^2)	derivative\:f(x)=\frac{4x}{(x-1)^{2}}
integral of (x^3+7)	\int\:(x^{3}+7)dx
(d^2)/(dx^2)(3csc(x))	\frac{d^{2}}{dx^{2}}(3\csc(x))
integral from-2 to 2 of 16-4x^2	\int\:_{-2}^{2}16-4x^{2}dx
integral of-(ln(x))/(x^2)	\int\:-\frac{\ln(x)}{x^{2}}dx
derivative of-72x	derivative\:-72x
integral of (y^2)/(1-y)	\int\:\frac{y^{2}}{1-y}dy
tangent of f(x)=3x-2x^{-1/2}+1,\at x=1	tangent\:f(x)=3x-2x^{-\frac{1}{2}}+1,\at\:x=1
10y^{''}+1000y=20cos(8t),y(0)=0,y^'(0)=0	10y^{\prime\:\prime\:}+1000y=20\cos(8t),y(0)=0,y^{\prime\:}(0)=0
derivative of y=3x-2	derivative\:y=3x-2
y^{''}+6y^'+34y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+34y=0
limit as x approaches 0 of (5x^3)/x	\lim\:_{x\to\:0}(\frac{5x^{3}}{x})
area 1/4 x^2,2x^2,x-3	area\:\frac{1}{4}x^{2},2x^{2},x-3
(\partial)/(\partial x)(6x(x^2+y^2+z^2)^2)	\frac{\partial\:}{\partial\:x}(6x(x^{2}+y^{2}+z^{2})^{2})
integral of ((2x^2+2))/((x^2-2x+2)^2)	\int\:\frac{(2x^{2}+2)}{(x^{2}-2x+2)^{2}}dx
tangent of f(x)=3x^4-x^3-5x^2+7,\at x=2	tangent\:f(x)=3x^{4}-x^{3}-5x^{2}+7,\at\:x=2
integral of x^4(7-(x^5)/(10))^3	\int\:x^{4}(7-\frac{x^{5}}{10})^{3}dx
integral of-xsin(y)	\int\:-x\sin(y)dy
integral of 3y	\int\:3ydy
area y=x,y=(7.25x)/(x^2+1)	area\:y=x,y=\frac{7.25x}{x^{2}+1}
derivative of f(x)=e^x(1-x)	derivative\:f(x)=e^{x}(1-x)
limit as x approaches infinity of 3+1/x	\lim\:_{x\to\:\infty\:}(3+\frac{1}{x})
derivative of-y/(x+y^2)	\frac{d}{dx}(-\frac{y}{x+y^{2}})
integral of (sin(t))/(cos^2(t))	\int\:\frac{\sin(t)}{\cos^{2}(t)}dt
integral of (29)/(x^3-27)	\int\:\frac{29}{x^{3}-27}dx
(dy)/(dx)+ycos(x)=7cos(x)	\frac{dy}{dx}+y\cos(x)=7\cos(x)
(\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8)	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+4xy+y^{6}}-8)
derivative of 4x^2e^{2x^2+x-1}	\frac{d}{dx}(4x^{2}e^{2x^{2}+x-1})
limit as x approaches-3 of 3x^2+5x+1	\lim\:_{x\to\:-3}(3x^{2}+5x+1)
derivative of (3x^3-2x^2(3x^4+x^2))	\frac{d}{dx}((3x^{3}-2x^{2})(3x^{4}+x^{2}))
integral from-a to a of sqrt(a^2-x^2)	\int\:_{-a}^{a}\sqrt{a^{2}-x^{2}}dx
limit as x approaches 1 of (x^2-5)/x	\lim\:_{x\to\:1}(\frac{x^{2}-5}{x})
integral of y(e^y)	\int\:y(e^{y})dy
derivative of ln(x+1-e^{3x})	\frac{d}{dx}(\ln(x+1)-e^{3x})
limit as x approaches-infinity of \sqrt[x]{2}	\lim\:_{x\to\:-\infty\:}(\sqrt[x]{2})
tangent of f(x)=x^2+9,(-4,25)	tangent\:f(x)=x^{2}+9,(-4,25)
integral of 1/((1-x)^4)	\int\:\frac{1}{(1-x)^{4}}dx
(\partial)/(\partial x)(8e^{ysqrt(x)}-x^2y^3)	\frac{\partial\:}{\partial\:x}(8e^{y\sqrt{x}}-x^{2}y^{3})
integral of 10e^{-10x}	\int\:10e^{-10x}dx
integral of-8/pi x	\int\:-\frac{8}{π}xdx
tangent of f(x)= 2/(1+e^{-x)},(0,1)	tangent\:f(x)=\frac{2}{1+e^{-x}},(0,1)
x^'=(x-17)^2	x^{\prime\:}=(x-17)^{2}
tangent of f(x)= 7/(x+8),(5, 7/13)	tangent\:f(x)=\frac{7}{x+8},(5,\frac{7}{13})
y^'=0.06(y-65)	y^{\prime\:}=0.06(y-65)
sum from n=1 to infinity of n/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n+1}
derivative of e^x+e^{-3x}	\frac{d}{dx}(e^{x}+e^{-3x})
(2dy)/(dx)+100y=30*sin(60x),y(0)=0	\frac{2\cdot\:dy}{dx}+100\cdot\:y=30\cdot\:\sin(60x),y(0)=0
derivative of sin(2x+3cos(2x))	\frac{d}{dx}(\sin(2x)+3\cos(2x))
8xy^'=2xe^x-8y+6x^2	8xy^{\prime\:}=2xe^{x}-8y+6x^{2}
limit as h approaches 0 of ((-5+h)-25)/h	\lim\:_{h\to\:0}(\frac{(-5+h)-25}{h})
limit as x approaches infinity of (i)^x	\lim\:_{x\to\:\infty\:}((i)^{x})
integral of (x^2)/((2-x^3)^2)	\int\:\frac{x^{2}}{(2-x^{3})^{2}}dx
derivative of sqrt(x^2+64)	\frac{d}{dx}(\sqrt{x^{2}+64})
(\partial)/(\partial z)(-3e^xcos(yz))	\frac{\partial\:}{\partial\:z}(-3e^{x}\cos(yz))
integral of (5+3x)/(1+x^2)	\int\:\frac{5+3x}{1+x^{2}}dx
integral of 15sqrt(x+1)	\int\:15\sqrt{x+1}dx
e^xy(dy)/(dx)=1	e^{x}y\frac{dy}{dx}=1
tangent of y= 2/x ,(-2,-1)	tangent\:y=\frac{2}{x},(-2,-1)
integral of x/(2x^3)	\int\:\frac{x}{2x^{3}}dx
limit as x approaches 1 of 5x^5-8x^3+8	\lim\:_{x\to\:1}(5x^{5}-8x^{3}+8)
integral of 3sin(4x)+4sin(3x)	\int\:3\sin(4x)+4\sin(3x)dx
(dy)/(dx)=x^3e^{x^4}	\frac{dy}{dx}=x^{3}e^{x^{4}}
limit as x approaches 2 of (2-x)^2	\lim\:_{x\to\:2}((2-x)^{2})
derivative of-4cos(2x)	derivative\:-4\cos(2x)
derivative of x^5e^xcos(x)	\frac{d}{dx}(x^{5}e^{x}\cos(x))
integral of sqrt(x^2-2x+5)	\int\:\sqrt{x^{2}-2x+5}dx
integral of 1/(x^2+3)	\int\:\frac{1}{x^{2}+3}dx
tangent of 1/(x-8)	tangent\:\frac{1}{x-8}
tangent of r=cos(2θ)	tangent\:r=\cos(2θ)
(\partial)/(\partial y)(y^4sin(3x))	\frac{\partial\:}{\partial\:y}(y^{4}\sin(3x))
integral of 1/(x^2+2x+6)	\int\:\frac{1}{x^{2}+2x+6}dx
integral of (e^{2t}+1/((t+1)^2))	\int\:(e^{2t}+\frac{1}{(t+1)^{2}})dt
inverse oflaplace (s-3)/(s^2+10s+9)	inverselaplace\:\frac{s-3}{s^{2}+10s+9}
limit as x approaches 4 of sqrt(2x+1)	\lim\:_{x\to\:4}(\sqrt{2x+1})
integral of 1/(-u^2+1)	\int\:\frac{1}{-u^{2}+1}du
derivative of ((x^8))/(8(1-x^2)^4)	derivative\:\frac{(x^{8})}{8(1-x^{2})^{4}}
derivative of 1/((9+x^2))	\frac{d}{dx}(\frac{1}{(9+x)^{2}})
derivative of x^{-3}+4x^{-5}-3x^{-8}	\frac{d}{dx}(x^{-3}+4x^{-5}-3x^{-8})
derivative of ln(6-5x)	\frac{d}{dx}(\ln(6-5x))
laplacetransform te^{,\at}	laplacetransform\:te^{,\at\:}
f^'(x)=\sqrt[3]{1-x^2}	f^{\prime\:}(x)=\sqrt[3]{1-x^{2}}
derivative of 20x^2	\frac{d}{dx}(20x^{2})
(d^2}{dx^2}(\frac{sin(x))/x)	\frac{d^{2}}{dx^{2}}(\frac{\sin(x)}{x})
y^{''}+8y^'+16y=0,y(0)=-4,y^'(0)=21	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0,y(0)=-4,y^{\prime\:}(0)=21
(d^2)/(dx^2)(x(3x+2)^5)	\frac{d^{2}}{dx^{2}}(x(3x+2)^{5})
derivative of y= x/(sqrt(x^2+5))	derivative\:y=\frac{x}{\sqrt{x^{2}+5}}
(\partial)/(\partial x)(1-y)	\frac{\partial\:}{\partial\:x}(1-y)
(\partial)/(\partial x)(a/(ln(x)-c))	\frac{\partial\:}{\partial\:x}(\frac{a}{\ln(x)-c})
y^'+(4y)/x =-4/x	y^{\prime\:}+\frac{4y}{x}=-\frac{4}{x}
tangent of f(x)=(6x)/(x^2-3),\at x=3	tangent\:f(x)=\frac{6x}{x^{2}-3},\at\:x=3
(\partial)/(\partial z)(ye^{xz})	\frac{\partial\:}{\partial\:z}(ye^{xz})
9y^{''}-6y^'+8y=0	9y^{\prime\:\prime\:}-6y^{\prime\:}+8y=0
(dy)/(dx)=3x^2(y-1)^3	\frac{dy}{dx}=3x^{2}(y-1)^{3}
derivative of 2(x-2^2)	\frac{d}{dx}(2(x-2)^{2})
laplacetransform sin^2(2t)	laplacetransform\:\sin^{2}(2t)
integral of ln(x-3)	\int\:\ln(x-3)dx
tangent of f(x)= 2/(x-5),\at x=7	tangent\:f(x)=\frac{2}{x-5},\at\:x=7

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