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Popular Calculus Problems

derivative of (1/2)^9	derivative\:(\frac{1}{2})^{9}
integral of (3x+1)/(x(x+1))	\int\:\frac{3x+1}{x(x+1)}dx
limit as x approaches 0+of cot(8)	\lim\:_{x\to\:0+}(\cot(8))
derivative of x^2cos^4(x)	derivative\:x^{2}\cos^{4}(x)
integral from 1 to 3 of (4z-z^2)	\int\:_{1}^{3}(4z-z^{2})dz
y^'+4y=2x	y^{\prime\:}+4y=2x
integral of (x^2)/((169+x^2)^2)	\int\:\frac{x^{2}}{(169+x^{2})^{2}}dx
sum from n=0 to infinity of nz^n	\sum\:_{n=0}^{\infty\:}nz^{n}
integral of ((2x+1))/((x+1)(x-2)(x-3))	\int\:\frac{(2x+1)}{(x+1)(x-2)(x-3)}dx
integral of sqrt(7-2x)	\int\:\sqrt{7-2x}dx
derivative of (3x^2tan(x)/(sec(x)))	\frac{d}{dx}(\frac{3x^{2}\tan(x)}{\sec(x)})
derivative of sin(sqrt(cos(tan(pix))))	derivative\:\sin(\sqrt{\cos(\tan(πx))})
derivative of (x^3-x+1^3)	\frac{d}{dx}((x^{3}-x+1)^{3})
limit as x approaches 2+of x/(x^2+4)	\lim\:_{x\to\:2+}(\frac{x}{x^{2}+4})
limit as x approaches 7 of (6x)/(x-7)	\lim\:_{x\to\:7}(\frac{6x}{x-7})
derivative of x^{-9cos(x})	\frac{d}{dx}(x^{-9\cos(x)})
3(dy)/(dt)=y-t^2y	3\frac{dy}{dt}=y-t^{2}y
(\partial)/(\partial x)(cos(4y-3x))	\frac{\partial\:}{\partial\:x}(\cos(4y-3x))
integral of sin(x)tan^2(x)	\int\:\sin(x)\tan^{2}(x)dx
integral of \sqrt[9]{x^8}	\int\:\sqrt[9]{x^{8}}dx
(\partial)/(\partial x)(x^2-2x)	\frac{\partial\:}{\partial\:x}(x^{2}-2x)
integral of (x^2+x-6)	\int\:(x^{2}+x-6)dx
integral of x/(25+4x^2)	\int\:\frac{x}{25+4x^{2}}dx
d/(dt)(k/t)	\frac{d}{dt}(\frac{k}{t})
derivative of e^{xy}(y+x(dy/(dx)))	\frac{d}{dx}(e^{xy}(y+x\frac{dy}{dx}))
integral of 6/(xln(x))	\int\:\frac{6}{x\ln(x)}dx
derivative of sqrt(x^5)-\sqrt[4]{x^9}	\frac{d}{dx}(\sqrt{x^{5}}-\sqrt[4]{x^{9}})
derivative of G(t)=(1-6t)/(2+t)	derivative\:G(t)=\frac{1-6t}{2+t}
sum from n=1 to infinity of (-3/4)^n	\sum\:_{n=1}^{\infty\:}(-\frac{3}{4})^{n}
limit as x approaches 0-of cos(x^2)	\lim\:_{x\to\:0-}(\cos(x^{2}))
integral from 0 to 3 of 1/(sqrt(4-t))	\int\:_{0}^{3}\frac{1}{\sqrt{4-t}}dt
(\partial)/(\partial x)(-z^2)	\frac{\partial\:}{\partial\:x}(-z^{2})
tangent of f(x)=sqrt(5x-1)	tangent\:f(x)=\sqrt{5x-1}
integral from-0.5 to 0 of 1.5x^2	\int\:_{-0.5}^{0}1.5x^{2}dx
x^2y^{''}-6xy^'+10y=0	x^{2}y^{\prime\:\prime\:}-6xy^{\prime\:}+10y=0
tangent of 4x^3-4x	tangent\:4x^{3}-4x
derivative of x^2-8ln(x)	\frac{d}{dx}(x^{2}-8\ln(x))
integral of sqrt(e^x)	\int\:\sqrt{e^{x}}dx
limit as x approaches 0-of (x^2)/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{x})
derivative of y=(4x-1)^3	derivative\:y=(4x-1)^{3}
tangent of y=7x-x^2,\at x=1	tangent\:y=7x-x^{2},\at\:x=1
f(x)=3^{cos(x)}	f(x)=3^{\cos(x)}
integral of tan(x)	\int\:\tan(x)dx
derivative of (1-e^x/(1+e^x))	\frac{d}{dx}(\frac{1-e^{x}}{1+e^{x}})
deg2rad (ln(x'))^'	deg2rad\:(\ln(x\prime\:))^{\prime\:}
f(x)=4sin(2x)+(2x^5-sqrt(x))/x	f(x)=4\sin(2x)+\frac{2x^{5}-\sqrt{x}}{x}
integral of (5sqrt(x^2-1))/(x^2)	\int\:\frac{5\sqrt{x^{2}-1}}{x^{2}}dx
tangent of y=5x-x^2,(1,4)	tangent\:y=5x-x^{2},(1,4)
limit as y approaches 1 of (y^2+3)/(y-1)	\lim\:_{y\to\:1}(\frac{y^{2}+3}{y-1})
integral of (8e^2x)-(3e^{-x})	\int\:(8e^{2}x)-(3e^{-x})dx
derivative of (2-2x^2(3x+1)^2)	\frac{d}{dx}((2-2x)^{2}(3x+1)^{2})
derivative of (a+bx/(c+dx))	\frac{d}{dx}(\frac{a+bx}{c+dx})
laplacetransform 3te^{-2t}	laplacetransform\:3te^{-2t}
derivative of 3(x-1^2)	\frac{d}{dx}(3(x-1)^{2})
integral of 1/(sin^4(x))	\int\:\frac{1}{\sin^{4}(x)}dx
derivative of {z}(x+x^2)	\frac{d}{dx}({z}(x)+x^{2})
integral from 0 to 1 of tsqrt(1+t^2+t^4)	\int\:_{0}^{1}t\sqrt{1+t^{2}+t^{4}}dt
limit as x approaches 3-of sin(pix)+1	\lim\:_{x\to\:3-}(\sin(πx)+1)
integral of e^{2x+e^x}	\int\:e^{2x+e^{x}}dx
limit as x approaches 1+of (x+10)/(x+2)	\lim\:_{x\to\:1+}(\frac{x+10}{x+2})
2xy(dy)/(dx)=y^2-x^2	2xy\frac{dy}{dx}=y^{2}-x^{2}
(dy)/(dx)=8xy+3y	\frac{dy}{dx}=8xy+3y
limit as x approaches 1 of 6	\lim\:_{x\to\:1}(6)
integral of sqrt((1-cos(x)))	\int\:\sqrt{(1-\cos(x))}dx
integral of 1/(x^3-27)	\int\:\frac{1}{x^{3}-27}dx
integral of (x^3+7x^2+25x+35)/(x^2+5x+6)	\int\:\frac{x^{3}+7x^{2}+25x+35}{x^{2}+5x+6}dx
integral of (4sinh(x))/(4+cosh^2(x))	\int\:\frac{4\sinh(x)}{4+\cosh^{2}(x)}dx
implicit (dy)/(dx),y=3x	implicit\:\frac{dy}{dx},y=3x
derivative of sqrt(x)+9/(sqrt(x))	\frac{d}{dx}(\sqrt{x}+\frac{9}{\sqrt{x}})
integral of (3-8x)	\int\:(3-8x)dx
derivative of 5\sqrt[3]{12x}	\frac{d}{dx}(5\sqrt[3]{12x})
derivative of (2x^3+8/x)	\frac{d}{dx}(\frac{2x^{3}+8}{x})
derivative of 8xcos(x^2)	\frac{d}{dx}(8x\cos(x^{2}))
limit as x approaches 8 of {f(7)g(-7)}	\lim\:_{x\to\:8}(\left\{f(7)g(-7)\right\})
integral of (4x^2+8)/(2x^2+1)	\int\:\frac{4x^{2}+8}{2x^{2}+1}dx
integral of 1/(xsqrt(25x^2-4))	\int\:\frac{1}{x\sqrt{25x^{2}-4}}dx
integral of (e^y)/(1-e^y)	\int\:\frac{e^{y}}{1-e^{y}}dy
limit as x approaches 0 of (0x^4+e^{0x})/(x^4)	\lim\:_{x\to\:0}(\frac{0x^{4}+e^{0x}}{x^{4}})
derivative of xln^2(x)	\frac{d}{dx}(x\ln^{2}(x))
derivative of (y+3/y)(y^2-5)	derivative\:(y+\frac{3}{y})(y^{2}-5)
derivative of sec^{n-2}(x)	\frac{d}{dx}(\sec^{n-2}(x))
limit as x approaches 0 of (10^x-1)/x	\lim\:_{x\to\:0}(\frac{10^{x}-1}{x})
derivative of (x^4+2)^2(x^5+4)^4	derivative\:(x^{4}+2)^{2}(x^{5}+4)^{4}
derivative of x^2-2x+5	derivative\:x^{2}-2x+5
integral from-infinity to 8 of xe^{x/4}	\int\:_{-\infty\:}^{8}xe^{\frac{x}{4}}dx
tangent of f(x)=2x^4-11x^2,\at x=1	tangent\:f(x)=2x^{4}-11x^{2},\at\:x=1
integral of x/(2x^2+3)	\int\:\frac{x}{2x^{2}+3}dx
7+e^{-5x}y^'=0	7+e^{-5x}y^{\prime\:}=0
integral of (2x-1)/((x-1)(x-2))	\int\:\frac{2x-1}{(x-1)(x-2)}dx
laplacetransform sin(w)	laplacetransform\:\sin(w)
y^{''}+4y^'+5y=15x+e^{(-x)}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=15x+e^{(-x)}
y^'=2xe^{(2y)}	y^{\prime\:}=2xe^{(2y)}
limit as x approaches pi/2-of sec(x)	\lim\:_{x\to\:\frac{π}{2}-}(\sec(x))
tangent of y=g(x),\at x=6	tangent\:y=g(x),\at\:x=6
inverse oflaplace 3/(s*(s^2+2s+5))	inverselaplace\:\frac{3}{s\cdot\:(s^{2}+2s+5)}
integral from 0 to 2pi of cos(x)cos(2x)	\int\:_{0}^{2π}\cos(x)\cos(2x)dx
integral of sin^3(x)cos^8(x)	\int\:\sin^{3}(x)\cos^{8}(x)dx
integral of (x^2-3)^2(2x)	\int\:(x^{2}-3)^{2}(2x)dx
limit as x approaches 0+of 1/(3x)	\lim\:_{x\to\:0+}(\frac{1}{3x})
integral of 9/(x^2+9)	\int\:\frac{9}{x^{2}+9}dx

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