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Popular Calculus Problems

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)}
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
integral of 1/(9-6x)	\int\:\frac{1}{9-6x}dx
integral of 1/(e^x-1)	\int\:\frac{1}{e^{x}-1}dx
integral of sin(x/2)	\int\:\sin(\frac{x}{2})dx
derivative of f(x)= 1/(cos(x))	derivative\:f(x)=\frac{1}{\cos(x)}
d/(dy)(2xy^4e^y+2xy^3+y)	\frac{d}{dy}(2xy^{4}e^{y}+2xy^{3}+y)
y^{''}+4y^'+6y=cos(x),y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=\cos(x),y(0)=0,y^{\prime\:}(0)=2
sum from n=1 to infinity of (x^n)/(2n-1)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{2n-1}
(\partial)/(\partial x)(e^{xz})	\frac{\partial\:}{\partial\:x}(e^{xz})
limit as x approaches 0+of (1-4x)^{1/x}	\lim\:_{x\to\:0+}((1-4x)^{\frac{1}{x}})
integral of 6x(3x^2+4)^4	\int\:6x(3x^{2}+4)^{4}dx
derivative of ((x-2^3)/(x^2))	\frac{d}{dx}(\frac{(x-2)^{3}}{x^{2}})
derivative of sqrt(3x)+\sqrt[3]{x}+1/x	\frac{d}{dx}(\sqrt{3x}+\sqrt[3]{x}+\frac{1}{x})
(\partial)/(\partial x)(x^3+y^3-3xy)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}-3xy)
tangent of f(x)=7e^xcos(x),\at x=0	tangent\:f(x)=7e^{x}\cos(x),\at\:x=0
limit as x approaches 0 of ((x-4)/(x+1))^{x-2}	\lim\:_{x\to\:0}((\frac{x-4}{x+1})^{x-2})
derivative of (sqrt(x)x/(x^2))	\frac{d}{dx}(\frac{\sqrt{x}x}{x^{2}})
y^'+3y=e^{-4t},y(0)=5	y^{\prime\:}+3y=e^{-4t},y(0)=5
derivative of 9/(e^x-e^{-x})	\frac{d}{dx}(\frac{9}{e^{x}-e^{-x}})
x^2+3y(dy)/(dx)=0	x^{2}+3y\frac{dy}{dx}=0
integral from 0 to 16 of 1/(sqrt(x))	\int\:_{0}^{16}\frac{1}{\sqrt{x}}dx
y^'=ry	y^{\prime\:}=ry
y^{''}=-2/(t^2)	y^{\prime\:\prime\:}=-\frac{2}{t^{2}}
tangent of y=x^2+5x+9,\at x=4	tangent\:y=x^{2}+5x+9,\at\:x=4
(\partial)/(\partial x)(yze^{xz}+e^{xz}+xye^{xz})	\frac{\partial\:}{\partial\:x}(yze^{xz}+e^{xz}+xye^{xz})
area y=1.2(x+0.1)^{0.5}+4,1,-0.1	area\:y=1.2(x+0.1)^{0.5}+4,1,-0.1
sum from n=0 to infinity of 2^n2^n	\sum\:_{n=0}^{\infty\:}2^{n}2^{n}
(\partial)/(\partial z)(x^2y^2z^2)	\frac{\partial\:}{\partial\:z}(x^{2}y^{2}z^{2})
tangent of x^2-3x+6,\at x=1	tangent\:x^{2}-3x+6,\at\:x=1
derivative of 7x^2-3/x+2sqrt(x)	\frac{d}{dx}(7x^{2}-\frac{3}{x}+2\sqrt{x})
derivative of (sqrt(x-3)/(sqrt(x+3)))	\frac{d}{dx}(\frac{\sqrt{x-3}}{\sqrt{x+3}})
derivative of sqrt(x^2+7)	derivative\:\sqrt{x^{2}+7}
integral of x^2sqrt(2x-1)	\int\:x^{2}\sqrt{2x-1}dx
(dx)/(dt)+t^7x^9+x/t =0	\frac{dx}{dt}+t^{7}x^{9}+\frac{x}{t}=0
(d^2)/(dx^2)(cos(sin(3θ)))	\frac{d^{2}}{dx^{2}}(\cos(\sin(3θ)))
tangent of f(x)=-(24)/((4x+1)),\at x=-1	tangent\:f(x)=-\frac{24}{(4x+1)},\at\:x=-1
derivative of (6e^w)/(7w)	derivative\:\frac{6e^{w}}{7w}
derivative of 14^{2x}	\frac{d}{dx}(14^{2x})
derivative of (5u)/(4u^2+1)	derivative\:\frac{5u}{4u^{2}+1}
tangent of f(x)=sqrt(x+2),\at x=2	tangent\:f(x)=\sqrt{x+2},\at\:x=2
taylor \sqrt[3]{1+x},0	taylor\:\sqrt[3]{1+x},0
tangent of x^3+x^2+6/x	tangent\:x^{3}+x^{2}+\frac{6}{x}
integral of (8x)/(x^2-3)	\int\:\frac{8x}{x^{2}-3}dx
integral of 1/(sin^2(2x)cos^2(2x))	\int\:\frac{1}{\sin^{2}(2x)\cos^{2}(2x)}dx
integral of sec^3(x)-sec(x)	\int\:\sec^{3}(x)-\sec(x)dx
integral from 0 to 1 of ((9t)/(1+t^2))	\int\:_{0}^{1}(\frac{9t}{1+t^{2}})dt
y^'=x(3-y)	y^{\prime\:}=x(3-y)
integral of (x^3(x^2-2x)^3)	\int\:(x^{3}(x^{2}-2x)^{3})dx
derivative of y= 1/2 (e^x-e^{-x})	derivative\:y=\frac{1}{2}(e^{x}-e^{-x})

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