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Popular Calculus Problems

(dy)/(dx)= 4/(xe^y)	\frac{dy}{dx}=\frac{4}{xe^{y}}
integral from 1 to 3 of 11r^3*ln(r)	\int\:_{1}^{3}11r^{3}\cdot\:\ln(r)dr
derivative of 6x^2*e^{(x^3)/3}	derivative\:6x^{2}\cdot\:e^{\frac{x^{3}}{3}}
derivative of sqrt(8x+\sqrt{9x)}	derivative\:\sqrt{8x+\sqrt{9x}}
laplacetransform (1+t)^7	laplacetransform\:(1+t)^{7}
integral of (x^2)/((x+1)^2)	\int\:\frac{x^{2}}{(x+1)^{2}}dx
integral from 1 to 6 of x^3ln(4x)	\int\:_{1}^{6}x^{3}\ln(4x)dx
inverse oflaplace ((s+1))/((s+2)^2)	inverselaplace\:\frac{(s+1)}{(s+2)^{2}}
integral of ((ln(x))^{22})/x	\int\:\frac{(\ln(x))^{22}}{x}dx
integral of x(15x+6)	\int\:x(15x+6)dx
integral of 1/((x-2)(x^2+4))	\int\:\frac{1}{(x-2)(x^{2}+4)}dx
d/(dt)(cos^3(t)+sin^3(t))	\frac{d}{dt}(\cos^{3}(t)+\sin^{3}(t))
(\partial)/(\partial z)(3e^xcos(yz))	\frac{\partial\:}{\partial\:z}(3e^{x}\cos(yz))
derivative of (5x/(7x^2+1))	\frac{d}{dx}(\frac{5x}{7x^{2}+1})
y^{''}+ay=0	y^{\prime\:\prime\:}+ay=0
sum from n=1 to infinity of n^2	\sum\:_{n=1}^{\infty\:}n^{2}
integral from-8 to 8 of sqrt(64-x^2)	\int\:_{-8}^{8}\sqrt{64-x^{2}}dx
(dy)/(dx)=3-6x+y-2xy	\frac{dy}{dx}=3-6x+y-2xy
tangent of (1+x)cos(x)	tangent\:(1+x)\cos(x)
integral of 7/(16+9r^2)	\int\:\frac{7}{16+9r^{2}}dr
derivative of (4x^3)	\frac{d}{dx}((4x)^{3})
tangent of y= 7/(sqrt(x)),(1,7)	tangent\:y=\frac{7}{\sqrt{x}},(1,7)
derivative of h(t)=(t^4-1)^3(t^3+1)^4	derivative\:h(t)=(t^{4}-1)^{3}(t^{3}+1)^{4}
derivative of (6x+8(4x+9)^5)	\frac{d}{dx}((6x+8)(4x+9)^{5})
derivative of xe^{-1/2 x}	\frac{d}{dx}(xe^{-\frac{1}{2}x})
(\partial)/(\partial x)(ln(x+7y+6z))	\frac{\partial\:}{\partial\:x}(\ln(x+7y+6z))
limit as x approaches 1 of (3sin(pix)-sin(3pix))/(x^3)	\lim\:_{x\to\:1}(\frac{3\sin(πx)-\sin(3πx)}{x^{3}})
inverse oflaplace (s-5)/(s^2-6s+25)	inverselaplace\:\frac{s-5}{s^{2}-6s+25}
laplacetransform t^2-10t+31	laplacetransform\:t^{2}-10t+31
integral of sqrt(1+4a^2x^2)	\int\:\sqrt{1+4a^{2}x^{2}}dx
integral of ln(x-2)	\int\:\ln(x-2)dx
tangent of y= 1/(x^3),(1,1)	tangent\:y=\frac{1}{x^{3}},(1,1)
tangent of f(x)=(5x)/(x-3),(4,20)	tangent\:f(x)=\frac{5x}{x-3},(4,20)
derivative of y=(x+5)^{1/x}	derivative\:y=(x+5)^{\frac{1}{x}}
integral of x^2(x^3+5)^9	\int\:x^{2}(x^{3}+5)^{9}dx
derivative of sqrt((x^2-1/(x^3-x)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-1}{x^{3}-x}})
integral of (3-6x)/(sqrt(25-9x^2))	\int\:\frac{3-6x}{\sqrt{25-9x^{2}}}dx
(\partial)/(\partial x)((x+y)e^{3x-4y})	\frac{\partial\:}{\partial\:x}((x+y)e^{3x-4y})
(d^2)/(dx^2)((e^x)/(8x+1))	\frac{d^{2}}{dx^{2}}(\frac{e^{x}}{8x+1})
derivative of ln(ln(x^2))	derivative\:\ln(\ln(x^{2}))
y^'-5/x y=(y^5)/(x^{11)}	y^{\prime\:}-\frac{5}{x}y=\frac{y^{5}}{x^{11}}
sum from n=1 to infinity of 4/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{4}{10^{n}}
derivative of (x^2/(x^4+1))	\frac{d}{dx}(\frac{x^{2}}{x^{4}+1})
area y=4-x^2,2x+y=4	area\:y=4-x^{2},2x+y=4
f(x)=x^2sin(x)	f(x)=x^{2}\sin(x)
integral of (2x+1)/(x^2+x-1)	\int\:\frac{2x+1}{x^{2}+x-1}dx
limit as x approaches 3+of (2x)/(x-3)	\lim\:_{x\to\:3+}(\frac{2x}{x-3})
(\partial)/(\partial x)(e^{-3x}sin(2t-3x))	\frac{\partial\:}{\partial\:x}(e^{-3x}\sin(2t-3x))
slope of 1/(4+3x)	slope\:\frac{1}{4+3x}
integral of (x^2)/(x^3-5)	\int\:\frac{x^{2}}{x^{3}-5}dx
taylor 1/(2x),\at 2	taylor\:\frac{1}{2x},\at\:2
limit as x approaches 0 of ((sin(2x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(2x))}{x})
(dy)/(dx)=-yx^2	\frac{dy}{dx}=-yx^{2}
derivative of-(x^2+3x-2^3)	\frac{d}{dx}(-(x^{2}+3x-2)^{3})
parity y=xsin(x)+cot(x)	parity\:y=x\sin(x)+\cot(x)
derivative of ((x+1^2)/((x-1)^2))	\frac{d}{dx}(\frac{(x+1)^{2}}{(x-1)^{2}})
derivative of z^3-5z+4	derivative\:z^{3}-5z+4
derivative of y=(x+2)/(x-2)	derivative\:y=\frac{x+2}{x-2}
integral of cos(10x)	\int\:\cos(10x)dx
dy=(9x+4y+1)^2dx	dy=(9x+4y+1)^{2}dx
integral of tan^2(x)sec^3(x)	\int\:\tan^{2}(x)\sec^{3}(x)dx
integral of 4+5/x	\int\:4+\frac{5}{x}dx
integral of (5-e^x)/(e^{3x)}	\int\:\frac{5-e^{x}}{e^{3x}}dx
integral of sin(x)2	\int\:\sin(x)2dx
integral of (e^{2x})/(1+e^{4x)}	\int\:\frac{e^{2x}}{1+e^{4x}}dx
integral of x^3(x+1)^5	\int\:x^{3}(x+1)^{5}dx
area y=x^2-9,y=7	area\:y=x^{2}-9,y=7
derivative of (x/7+7/x)^7	derivative\:(\frac{x}{7}+\frac{7}{x})^{7}
integral of [x^2cos(x)]	\int\:[x^{2}\cos(x)]dx
derivative of 9x^8e^x+e^{xx^9}	\frac{d}{dx}(9x^{8}e^{x}+e^{xx^{9}})
derivative of (y^4)/4+1/(8y^2)	derivative\:\frac{y^{4}}{4}+\frac{1}{8y^{2}}
integral from 1 to 4 of-9e^{sqrt(x)}	\int\:_{1}^{4}-9e^{\sqrt{x}}dx
slope of (-3,7),(2,-6)	slope\:(-3,7),(2,-6)
integral of 4xe^{6x}	\int\:4xe^{6x}dx
area-1/2 x^2+5/2 x-2,[-2,7]	area\:-\frac{1}{2}x^{2}+\frac{5}{2}x-2,[-2,7]
f(x)=(1+x)/((2x^2+1)^2)	f(x)=\frac{1+x}{(2x^{2}+1)^{2}}
y^'+2y=0,y(1)=1	y^{\prime\:}+2y=0,y(1)=1
yy^'= x/(x^2+1)	yy^{\prime\:}=\frac{x}{x^{2}+1}
y^'+y=e^x	y^{\prime\:}+y=e^{x}
laplacetransform e^tt	laplacetransform\:e^{t}t
integral of (1-cos(x))/(csc^2(x))	\int\:\frac{1-\cos(x)}{\csc^{2}(x)}dx
derivative of (8x+3^2)	\frac{d}{dx}((8x+3)^{2})
derivative of (3x^4+1^3)	\frac{d}{dx}((3x^{4}+1)^{3})
integral of sec^2(x)tan(x)	\int\:\sec^{2}(x)\tan(x)dx
derivative of (C^2-x^2/(2x))	\frac{d}{dx}(\frac{C^{2}-x^{2}}{2x})
y^{''}=x,y(-1)=0,y(1)=0	y^{\prime\:\prime\:}=x,y(-1)=0,y(1)=0
integral from 0 to pi/6 of sin^5(3x)	\int\:_{0}^{\frac{π}{6}}\sin^{5}(3x)dx
derivative of-4e^{3x}	\frac{d}{dx}(-4e^{3x})
integral of (x^2)/(sqrt(256-64x^2))	\int\:\frac{x^{2}}{\sqrt{256-64x^{2}}}dx
tangent of f(x)=x^3,\at x=-4	tangent\:f(x)=x^{3},\at\:x=-4
derivative of arccos({f}(x))	\frac{d}{dx}(\arccos({f}(x)))
derivative of-2asin(2x+bcos(2x)*2)	\frac{d}{dx}(-2a\sin(2x)+b\cos(2x)\cdot\:2)
limit as x approaches 0+of (l(x))/(x^3)	\lim\:_{x\to\:0+}(\frac{l(x)}{x^{3}})
limit as x approaches 8 of 4/((x-8)^2)	\lim\:_{x\to\:8}(\frac{4}{(x-8)^{2}})
derivative of cos^3(x+sin^4(x))	\frac{d}{dx}(\cos^{3}(x)+\sin^{4}(x))
(\partial)/(\partial x)(8ln(cos(x)))	\frac{\partial\:}{\partial\:x}(8\ln(\cos(x)))
(\partial)/(\partial x)(5sin(3x)cos(4y))	\frac{\partial\:}{\partial\:x}(5\sin(3x)\cos(4y))
y^'=-2y+5t,y(0)=-4	y^{\prime\:}=-2y+5t,y(0)=-4
integral of e^{9x}cos(8x)	\int\:e^{9x}\cos(8x)dx
(\partial)/(\partial z)(2x^{y/z})	\frac{\partial\:}{\partial\:z}(2x^{\frac{y}{z}})

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