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Popular Calculus Problems

integral of 7x^6-6/(x^6)	\int\:7x^{6}-\frac{6}{x^{6}}dx
integral of sqrt(5+2x)	\int\:\sqrt{5+2x}dx
limit as h approaches 0 of ((a+h)-(a))/h	\lim\:_{h\to\:0}(\frac{(a+h)-(a)}{h})
sum from n=1 to infinity of (5)^{-n}	\sum\:_{n=1}^{\infty\:}(5)^{-n}
integral from-3 to 3 of sin(x)x	\int\:_{-3}^{3}\sin(x)xdx
derivative of x^{9/2}	\frac{d}{dx}(x^{\frac{9}{2}})
integral of u/(sqrt(1-u^2))	\int\:\frac{u}{\sqrt{1-u^{2}}}du
2xdy-2ydx=sqrt(x^2+4y^2)dx	2xdy-2ydx=\sqrt{x^{2}+4y^{2}}dx
integral of (x^2)/(sqrt(25+x^6))	\int\:\frac{x^{2}}{\sqrt{25+x^{6}}}dx
(\partial)/(\partial x)(e^{-4t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-4t}\cos(πx))
tangent of y=(sqrt(x))/(x+4),(1,0.2)	tangent\:y=\frac{\sqrt{x}}{x+4},(1,0.2)
d/(dy)(-2y)	\frac{d}{dy}(-2y)
laplacetransform (1-3sin(4t))^2	laplacetransform\:(1-3\sin(4t))^{2}
derivative of 3x-1	derivative\:3x-1
(\partial)/(\partial x)(ln(16x^2-13y^2))	\frac{\partial\:}{\partial\:x}(\ln(16x^{2}-13y^{2}))
extreme f(y)=2x^2+3xy+4y^2+5x+6y-7	extreme\:f(y)=2x^{2}+3xy+4y^{2}+5x+6y-7
(x^2+y^2-3)dx=(y+xy)dy,y(0)=1	(x^{2}+y^{2}-3)dx=(y+xy)dy,y(0)=1
(dy)/(dx)=1+e^{y-x+5}	\frac{dy}{dx}=1+e^{y-x+5}
d/(dy)(sqrt(y/3))	\frac{d}{dy}(\sqrt{\frac{y}{3}})
limit as x approaches infinity of 4-1/x	\lim\:_{x\to\:\infty\:}(4-\frac{1}{x})
integral of (sec^2(x))/(tan^2(x))	\int\:\frac{\sec^{2}(x)}{\tan^{2}(x)}dx
limit as x approaches-4 of 3x+1	\lim\:_{x\to\:-4}(3x+1)
(\partial)/(\partial h)(2pirh+pir^2)	\frac{\partial\:}{\partial\:h}(2πrh+πr^{2})
derivative of (2y/(3x^2+2y^2))	\frac{d}{dx}(\frac{2y}{3x^{2}+2y^{2}})
y^{''}+14y^'+85y=0	y^{\prime\:\prime\:}+14y^{\prime\:}+85y=0
derivative of (3x+2)/(4x)	derivative\:\frac{3x+2}{4x}
limit as x approaches 3 of x+3x-3	\lim\:_{x\to\:3}(x+3x-3)
integral from-3 to 0 of xsqrt(1-x)	\int\:_{-3}^{0}x\sqrt{1-x}dx
integral of 6xe^x	\int\:6xe^{x}dx
derivative of 8^xln(x)	\frac{d}{dx}(8^{x}\ln(x))
(\partial)/(\partial x)(e^{6x+7y})	\frac{\partial\:}{\partial\:x}(e^{6x+7y})
derivative of 2/(1-6x)	\frac{d}{dx}(\frac{2}{1-6x})
integral of 1/9	\int\:\frac{1}{9}
integral from 0 to 1 of y/(e^{4y)}	\int\:_{0}^{1}\frac{y}{e^{4y}}dy
derivative of xsqrt(x+6)	\frac{d}{dx}(x\sqrt{x+6})
limit as x approaches infinity of-1/x+1	\lim\:_{x\to\:\infty\:}(-\frac{1}{x}+1)
derivative of f(x)=ln((sqrt(4+x^2))/x)	derivative\:f(x)=\ln(\frac{\sqrt{4+x^{2}}}{x})
tangent of f(x)=20sqrt(x),(4,40)	tangent\:f(x)=20\sqrt{x},(4,40)
y^{''}+5y^'-2y=0	y^{\prime\:\prime\:}+5y^{\prime\:}-2y=0
integral of 1/(sqrt(t^2-12t+40))	\int\:\frac{1}{\sqrt{t^{2}-12t+40}}dt
limit as x approaches 0-of 1/(sqrt(1/x))	\lim\:_{x\to\:0-}(\frac{1}{\sqrt{\frac{1}{x}}})
derivative of (t^6+26t^4-t^3+179)^{73}	derivative\:(t^{6}+26t^{4}-t^{3}+179)^{73}
limit as x approaches 0 of (1+4/x)^x	\lim\:_{x\to\:0}((1+\frac{4}{x})^{x})
slope ofintercept (0,32),(100,212)	slopeintercept\:(0,32),(100,212)
d/(dt)((e^t)/(4-3e^t))	\frac{d}{dt}(\frac{e^{t}}{4-3e^{t}})
sum from n=0 to infinity of n/(2^n)x^n	\sum\:_{n=0}^{\infty\:}\frac{n}{2^{n}}x^{n}
integral from 0 to 1 of 1-x	\int\:_{0}^{1}1-xdx
(\partial)/(\partial x)(xyw)	\frac{\partial\:}{\partial\:x}(xyw)
derivative of cos(2y-3x^2y^2)	\frac{d}{dx}(\cos(2y)-3x^{2}y^{2})
integral of x(x^2+5)^3	\int\:x(x^{2}+5)^{3}dx
integral from 0 to 1 of 1/((x^2+1)^2)	\int\:_{0}^{1}\frac{1}{(x^{2}+1)^{2}}dx
derivative of (1-2x^3/((1+x^3)^2))	\frac{d}{dx}(\frac{1-2x^{3}}{(1+x^{3})^{2}})
derivative of (arctan(8x))^2	derivative\:(\arctan(8x))^{2}
integral from 1 to e^2 of ln(x)	\int\:_{1}^{e^{2}}\ln(x)dx
y^{''}+14y^'+58y=0	y^{\prime\:\prime\:}+14y^{\prime\:}+58y=0
derivative of 1/(2sqrt(x))+1/(7x^{6/7)}	derivative\:\frac{1}{2\sqrt{x}}+\frac{1}{7x^{\frac{6}{7}}}
integral of 2(x-2)*ln(x-2)	\int\:2(x-2)\cdot\:\ln(x-2)dx
integral of 1/(4-6x)	\int\:\frac{1}{4-6x}dx
dx+dy+xdy=ydx	dx+dy+xdy=ydx
f(x)=(2pi-xcos(x))/(x-2pi)	f(x)=\frac{2π-x\cos(x)}{x-2π}
limit as x approaches+1 of (x-1)/(x^2-x)	\lim\:_{x\to\:+1}(\frac{x-1}{x^{2}-x})
x(dy)/(dx)=8y	x\frac{dy}{dx}=8y
derivative of-1/(2x)	\frac{d}{dx}(-\frac{1}{2x})
integral of (5-4x)/(sqrt(12x-4x^2-8))	\int\:\frac{5-4x}{\sqrt{12x-4x^{2}-8}}dx
5(ln(y))y^'-x^7y=0	5(\ln(y))y^{\prime\:}-x^{7}y=0
integral of (-1)/(1+9x^2)	\int\:\frac{-1}{1+9x^{2}}dx
slope of (-5,-5),(0,-7)	slope\:(-5,-5),(0,-7)
derivative of (3x-2x^2^3)	\frac{d}{dx}((3x-2x^{2})^{3})
limit as x approaches infinity of 1.04^x	\lim\:_{x\to\:\infty\:}(1.04^{x})
integral of 5x^2sin(8x)	\int\:5x^{2}\sin(8x)dx
(\partial)/(\partial x)(6xy^3z^3+7xyz)	\frac{\partial\:}{\partial\:x}(6xy^{3}z^{3}+7xyz)
(dy)/(dx)=0.75y	\frac{dy}{dx}=0.75y
(dy)/(dx)+6xy^4=0	\frac{dy}{dx}+6xy^{4}=0
(dr}{dθ}=\frac{r^2)/θ ,r(1)=2	\frac{dr}{dθ}=\frac{r^{2}}{θ},r(1)=2
derivative of \sqrt[3]{-e^{-x}}	\frac{d}{dx}(\sqrt[3]{-e^{-x}})
integral of (x^2)/8	\int\:\frac{x^{2}}{8}dx
tangent of y= 5/x ,(1/2 ,10)	tangent\:y=\frac{5}{x},(\frac{1}{2},10)
integral of x^2sin(θ)	\int\:x^{2}\sin(θ)dx
integral of (7x^2)/((225+x^2)^2)	\int\:\frac{7x^{2}}{(225+x^{2})^{2}}dx
limit as x approaches 0+of (5x^2)(ln(x))	\lim\:_{x\to\:0+}((5x^{2})(\ln(x)))
tangent of y=(x^2-1)/(x^2+x+1),\at x=1	tangent\:y=\frac{x^{2}-1}{x^{2}+x+1},\at\:x=1
integral of 4-4sin(x)+sin^2(x)	\int\:4-4\sin(x)+\sin^{2}(x)dx
integral of sqrt(64-3x^2)	\int\:\sqrt{64-3x^{2}}dx
(\partial)/(\partial x)(x^2e^2)	\frac{\partial\:}{\partial\:x}(x^{2}e^{2})
limit as x approaches 1 of (ax)/3	\lim\:_{x\to\:1}(\frac{ax}{3})
y^'=((4x^3+1))/(2y-6)	y^{\prime\:}=\frac{(4x^{3}+1)}{2y-6}
limit as x approaches 2 of (x^3-4)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{3}-4}{x-2})
8x^2y^'=y^'+2xe^{-y}	8x^{2}y^{\prime\:}=y^{\prime\:}+2xe^{-y}
inverse oflaplace (s+3)/(s^2+s+3)	inverselaplace\:\frac{s+3}{s^{2}+s+3}
integral of x^3(x^4-1)^2	\int\:x^{3}(x^{4}-1)^{2}dx
integral of 8cos(4x)	\int\:8\cos(4x)dx
derivative of (x^3/(x+1))	\frac{d}{dx}(\frac{x^{3}}{x+1})
limit as x approaches 0 of x^{3sin(x)}	\lim\:_{x\to\:0}(x^{3\sin(x)})
integral of (7x^3-2x^2+4)	\int\:(7x^{3}-2x^{2}+4)dx
integral of 9tan^2(x)	\int\:9\tan^{2}(x)dx
integral from-1 to 2 of 1/(x^4)	\int\:_{-1}^{2}\frac{1}{x^{4}}dx
y^{''}+2y^'+y=0,y(1)=1,y^'(1)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(1)=1,y^{\prime\:}(1)=0
derivative of x^4-4x^3+3x^2-3	\frac{d}{dx}(x^{4}-4x^{3}+3x^{2}-3)
integral of (x^2-2x+5)e^{-x}	\int\:(x^{2}-2x+5)e^{-x}dx
limit as x approaches-2 of 7x^2+8	\lim\:_{x\to\:-2}(7x^{2}+8)

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