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Popular Calculus Problems

integral of ((x+1)(x-1))/(x^2)	\int\:\frac{(x+1)(x-1)}{x^{2}}dx
derivative of log_{9}(ln(x))	derivative\:\log_{9}(\ln(x))
limit as x approaches+0 of 8/(6+e^x)	\lim\:_{x\to\:+0}(\frac{8}{6+e^{x}})
integral from 1 to infinity of 3/(x^4)	\int\:_{1}^{\infty\:}\frac{3}{x^{4}}dx
derivative of ((17-x)sqrt(2x+8))/2	derivative\:\frac{(17-x)\sqrt{2x+8}}{2}
limit as x approaches-1 of x^4-2x^2-1	\lim\:_{x\to\:-1}(x^{4}-2x^{2}-1)
integral from 0 to 0.6 of (600x)	\int\:_{0}^{0.6}(600x)dx
(dy)/(dx)=((sec(y)))/((x-1)^2)	\frac{dy}{dx}=\frac{(\sec(y))}{(x-1)^{2}}
integral from 0 to pi of sin^5(x)	\int\:_{0}^{π}\sin^{5}(x)dx
integral of \sqrt[3]{x}+1/(\sqrt[3]{x)}	\int\:\sqrt[3]{x}+\frac{1}{\sqrt[3]{x}}dx
inverse oflaplace s/((s+1))	inverselaplace\:\frac{s}{(s+1)}
(\partial)/(\partial z)(x^{yz})	\frac{\partial\:}{\partial\:z}(x^{yz})
derivative of 11arccot(x+11arccot(1/x))	\frac{d}{dx}(11\arccot(x)+11\arccot(\frac{1}{x}))
derivative of (-5)/((2x^3+7)^2)	derivative\:\frac{-5}{(2x^{3}+7)^{2}}
slope of (2,7),(-5,2)	slope\:(2,7),(-5,2)
y^{''}-9y^'=0	y^{\prime\:\prime\:}-9y^{\prime\:}=0
integral of sin(2x)sqrt(1+cos^2(x))	\int\:\sin(2x)\sqrt{1+\cos^{2}(x)}dx
(dy}{dx}=\frac{x^2-2y)/x	\frac{dy}{dx}=\frac{x^{2}-2y}{x}
limit as x approaches 2 of (2x+1)/(x-2)	\lim\:_{x\to\:2}(\frac{2x+1}{x-2})
derivative of sin(sqrt(3)x)	\frac{d}{dx}(\sin(\sqrt{3}x))
sum from n=1 to infinity of (2/3)^{n+2}	\sum\:_{n=1}^{\infty\:}(\frac{2}{3})^{n+2}
(\partial)/(\partial x)((-1)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{-1}{x^{2}+y^{2}})
laplacetransform e^{-3t}+3+2t+4t^2+5t^3	laplacetransform\:e^{-3t}+3+2t+4t^{2}+5t^{3}
derivative of sin(2x+cos(x))	\frac{d}{dx}(\sin(2x)+\cos(x))
integral of cos(x/(sqrt(2)))	\int\:\cos(\frac{x}{\sqrt{2}})dx
(1+x)dy-ydx=0	(1+x)dy-ydx=0
limit as x approaches infinity of 6^x	\lim\:_{x\to\:\infty\:}(6^{x})
limit as x approaches 0-of f(x)	\lim\:_{x\to\:0-}(f(x))
derivative of f(x)=-3e^{x+1}	derivative\:f(x)=-3e^{x+1}
tangent of f(x)=8x-x^2	tangent\:f(x)=8x-x^{2}
limit as x approaches 0+of 1/(x+1)	\lim\:_{x\to\:0+}(\frac{1}{x+1})
(\partial)/(\partial x)(1-x^2-y^2)	\frac{\partial\:}{\partial\:x}(1-x^{2}-y^{2})
limit as x approaches 1 of sqrt(x)-x	\lim\:_{x\to\:1}(\sqrt{x}-x)
(\partial)/(\partial x)(4x^{-1})	\frac{\partial\:}{\partial\:x}(4x^{-1})
tangent of f(x)=x^2+6x,\at a=3	tangent\:f(x)=x^{2}+6x,\at\:a=3
limit as x approaches 2 of sqrt(3x-2)	\lim\:_{x\to\:2}(\sqrt{3x-2})
derivative of (x^2)/(8+x)	derivative\:\frac{x^{2}}{8+x}
integral from 0 to 1 of 23cos(x^2)	\int\:_{0}^{1}23\cos(x^{2})dx
derivative of (tan(x)^{1/x})	\frac{d}{dx}((\tan(x))^{\frac{1}{x}})
integral of 1/(x^2+5x-6)	\int\:\frac{1}{x^{2}+5x-6}dx
derivative of 2cx	\frac{d}{dx}(2cx)
integral of 1/(x(ln(x^4))^9)	\int\:\frac{1}{x(\ln(x^{4}))^{9}}dx
e^xy(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-2x-y}
laplacetransform 3sin(sqrt(2)t)	laplacetransform\:3\sin(\sqrt{2}t)
integral of-2x^{-4}	\int\:-2x^{-4}dx
derivative of f(x)=((5^{3x^7})/(8x^2))^4	derivative\:f(x)=(\frac{5^{3x^{7}}}{8x^{2}})^{4}
integral of (x-3)/(x^2-12x+36)	\int\:\frac{x-3}{x^{2}-12x+36}dx
sum from n=1 to infinity of n/(n+3)	\sum\:_{n=1}^{\infty\:}\frac{n}{n+3}
tangent of f(x)=(2+4x)(5-4x),\at x=1	tangent\:f(x)=(2+4x)(5-4x),\at\:x=1
tangent of y=2x^3-2x^2-2x	tangent\:y=2x^{3}-2x^{2}-2x
(dy)/(dx)+y/x =x^3	\frac{dy}{dx}+\frac{y}{x}=x^{3}
derivative of (e^{ax^2+bx+c}/x)	\frac{d}{dx}(\frac{e^{ax^{2}+bx+c}}{x})
limit as e approaches 1 of 5ln^2(e)	\lim\:_{e\to\:1}(5\ln^{2}(e))
limit as x approaches+0 of (1-1/x)x	\lim\:_{x\to\:+0}((1-\frac{1}{x})x)
(\partial)/(\partial y)(x+y+1)	\frac{\partial\:}{\partial\:y}(x+y+1)
integral of 1/(x^{2022)}	\int\:\frac{1}{x^{2022}}dx
d/(dt)(7t^3)	\frac{d}{dt}(7t^{3})
inverse oflaplace 1/(s(4s^2-1))	inverselaplace\:\frac{1}{s(4s^{2}-1)}
integral of 1/(x^2-6x)	\int\:\frac{1}{x^{2}-6x}dx
integral of 1/(4x+xln^2(3x))	\int\:\frac{1}{4x+x\ln^{2}(3x)}dx
integral of sec(t)(2sec(t)+7tan(t))	\int\:\sec(t)(2\sec(t)+7\tan(t))dt
integral of (6x^3+4x^2-2x)/(2x^2)	\int\:\frac{6x^{3}+4x^{2}-2x}{2x^{2}}dx
(\partial)/(\partial x)(x^3-xsin(y))	\frac{\partial\:}{\partial\:x}(x^{3}-x\sin(y))
integral from-1 to 0 of x^3-x	\int\:_{-1}^{0}x^{3}-xdx
limit as x approaches 2 of (5x)/(x-2)	\lim\:_{x\to\:2}(\frac{5x}{x-2})
integral of e^{2θ}sin(3θ)	\int\:e^{2θ}\sin(3θ)dθ
(ln(f(x)))\prime	(\ln(f(x)))\prime
inverse oflaplace 10s	inverselaplace\:10s
(3^{-x^2})^'	(3^{-x^{2}})^{\prime\:}
derivative of 1-(36)/(x^2)	derivative\:1-\frac{36}{x^{2}}
(dx)/(dt)=ax+b	\frac{dx}{dt}=ax+b
-2y^{''}+4y^'+3y=1	-2y^{\prime\:\prime\:}+4y^{\prime\:}+3y=1
f(x)=(x^2+2)(x^4+1)	f(x)=(x^{2}+2)(x^{4}+1)
cos(t)y^'-sin(t)y=t^2	\cos(t)y^{\prime\:}-\sin(t)y=t^{2}
simplify x/(x+c/x)	simplify\:\frac{x}{x+\frac{c}{x}}
derivative of sqrt(7)x+sqrt(6x)	derivative\:\sqrt{7}x+\sqrt{6x}
tangent of f(x)=5x^{3/5}-4	tangent\:f(x)=5x^{\frac{3}{5}}-4
integral of (Inx)/((x+1)^2)	\int\:\frac{Inx}{(x+1)^{2}}dx
limit as x approaches infinity of 4-x^2	\lim\:_{x\to\:\infty\:}(4-x^{2})
derivative of 2sec(3x^2)	\frac{d}{dx}(2\sec(3x^{2}))
tangent of y=(x^3-9x)^{12}	tangent\:y=(x^{3}-9x)^{12}
integral of csc^4(4x)	\int\:\csc^{4}(4x)dx
derivative of (4-sqrt(x)^2)	\frac{d}{dx}((4-\sqrt{x})^{2})
integral of (100)/(25+(5y)^2)+e^4	\int\:\frac{100}{25+(5y)^{2}}+e^{4}dy
derivative of (y(4x+4y))/((x^2+y^2))	derivative\:\frac{y(4x+4y)}{(x^{2}+y^{2})}
integral from 1 to 4 of x^2+2	\int\:_{1}^{4}x^{2}+2dx
(\partial)/(\partial x)(2x^{3y})	\frac{\partial\:}{\partial\:x}(2x^{3y})
(\partial)/(\partial t)(-3st)	\frac{\partial\:}{\partial\:t}(-3st)
tangent of (0.1666)(0.998)^x	tangent\:(0.1666)(0.998)^{x}
derivative of (2x^2-5x+4/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}-5x+4}{\sqrt{x}})
area y=sqrt(x+4),y= x/2+2	area\:y=\sqrt{x+4},y=\frac{x}{2}+2
integral of 8tan^4(xse)c^6x	\int\:8\tan^{4}(xse)c^{6}xdx
derivative of e^{1/2 x}	derivative\:e^{\frac{1}{2}x}
area 4-4cos(7x),4cos(7x),0>= x>= pi/7	area\:4-4\cos(7x),4\cos(7x),0\ge\:x\ge\:\frac{π}{7}
derivative of 2xsqrt(x)+1/(sqrt(x))	\frac{d}{dx}(2x\sqrt{x}+\frac{1}{\sqrt{x}})
integral of x^2+7	\int\:x^{2}+7dx
y^{''}=-3y-2y^',y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}=-3y-2y^{\prime\:},y(0)=1,y^{\prime\:}(0)=0
integral of 4/(1+x^2)	\int\:\frac{4}{1+x^{2}}dx
3y^'-2y=e^{-pi/2}	3y^{\prime\:}-2y=e^{-\frac{π}{2}}
derivative of y=x^{2cos(x)}	derivative\:y=x^{2\cos(x)}

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