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Popular Calculus Problems

integral of 1/(4x-1)	\int\:\frac{1}{4x-1}dx
2y^{''}-8y=0,y(-2)=2,y^'(-2)=1	2y^{\prime\:\prime\:}-8y=0,y(-2)=2,y^{\prime\:}(-2)=1
f(x)=ln(x+sqrt(x^2-1))	f(x)=\ln(x+\sqrt{x^{2}-1})
integral of (6x-5)	\int\:(6x-5)dx
(y+4)(dy)/(dx)=2xy+4y	(y+4)\frac{dy}{dx}=2xy+4y
integral of (cos(6x)-csc^2(x))	\int\:(\cos(6x)-\csc^{2}(x))dx
derivative of (4+sec(θ))sin(θ)	derivative\:(4+\sec(θ))\sin(θ)
integral from 1 to 5 of 6/x	\int\:_{1}^{5}\frac{6}{x}dx
d/(d{x)}(({x})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{x}}(\frac{{x}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
integral from 2 to 5 of x	\int\:_{2}^{5}xdx
sum from n=1 to infinity of ln(1)	\sum\:_{n=1}^{\infty\:}\ln(1)
derivative of (x^2+x^6)	\frac{d}{dx}((x^{2}+x)^{6})
area y=6-6x^2,y=0	area\:y=6-6x^{2},y=0
limit as x approaches 0 of (cos(x))^{csc(x)}	\lim\:_{x\to\:0}((\cos(x))^{\csc(x)})
derivative of ((-x^2-1)/((x^2-1)^2))	\frac{d}{dx}(\frac{(-x^{2}-1)}{(x^{2}-1)^{2}})
integral of 3x^{-1}	\int\:3x^{-1}dx
2xydx+(x^2-1)dy=0	2xydx+(x^{2}-1)dy=0
f(x)=(cos(x))/(1+sin(x))	f(x)=\frac{\cos(x)}{1+\sin(x)}
(\partial)/(\partial x)(x^2y+y^3)	\frac{\partial\:}{\partial\:x}(x^{2}y+y^{3})
area-x^2+1.907,0,0.266	area\:-x^{2}+1.907,0,0.266
integral from 0 to 1 of (5e^x-5xe^{x^2})	\int\:_{0}^{1}(5e^{x}-5xe^{x^{2}})dx
(dy)/(dx)(x+2)+y=3	\frac{dy}{dx}(x+2)+y=3
derivative of x^{-2x}	\frac{d}{dx}(x^{-2x})
limit as x approaches 0 of x^8cos(5/x)	\lim\:_{x\to\:0}(x^{8}\cos(\frac{5}{x}))
(d^2y)/(dt^2)+y=0	\frac{d^{2}y}{dt^{2}}+y=0
limit as x approaches 0 of (sin(3x))/3	\lim\:_{x\to\:0}(\frac{\sin(3x)}{3})
(dy)/(dx)=((x^2+3y^2))/((2xy))	\frac{dy}{dx}=\frac{(x^{2}+3y^{2})}{(2xy)}
(dy)/(dx)=2+sqrt(3+y-2x)	\frac{dy}{dx}=2+\sqrt{3+y-2x}
limit as x approaches 0 of-2/(sqrt(x))	\lim\:_{x\to\:0}(-\frac{2}{\sqrt{x}})
integral from 0 to 1 of (e^x+1)^2	\int\:_{0}^{1}(e^{x}+1)^{2}dx
tangent of y=8x^4,\at x=2	tangent\:y=8x^{4},\at\:x=2
tangent of f(x)=(x^3-4x)^8,\at x=2	tangent\:f(x)=(x^{3}-4x)^{8},\at\:x=2
integral of 2x^2sqrt(1-x^3)	\int\:2x^{2}\sqrt{1-x^{3}}dx
(\partial)/(\partial x)(3xy+y^2)	\frac{\partial\:}{\partial\:x}(3xy+y^{2})
integral of (2-3e^x)	\int\:(2-3e^{x})dx
integral of (x+1)/(x^3-6x^2+9x)	\int\:\frac{x+1}{x^{3}-6x^{2}+9x}dx
limit as x approaches 0 of-((6x)/(x^4))	\lim\:_{x\to\:0}(-(\frac{6x}{x^{4}}))
integral of xe^{-x/(10)}	\int\:xe^{-\frac{x}{10}}dx
integral from 0 to 2 of 2e^x	\int\:_{0}^{2}2e^{x}dx
derivative of (3t-1)(2t-2)^{-1}	derivative\:(3t-1)(2t-2)^{-1}
limit as x approaches 2 of 3x^2-4x+5	\lim\:_{x\to\:2}(3x^{2}-4x+5)
(\partial)/(\partial z)(sin(z))	\frac{\partial\:}{\partial\:z}(\sin(z))
derivative of (x^7+4)/(x^7)	derivative\:\frac{x^{7}+4}{x^{7}}
derivative of (5x/(x-1))	\frac{d}{dx}(\frac{5x}{x-1})
derivative of e^-	\frac{d}{dx}(e^{-})
taylor 5sin^2(x)	taylor\:5\sin^{2}(x)
derivative of y=(6x-5)^2(3-x^5)^2	derivative\:y=(6x-5)^{2}(3-x^{5})^{2}
limit as x approaches-1 of x^3+1	\lim\:_{x\to\:-1}(x^{3}+1)
limit as x approaches 0 of (1-cos(8x))/(4x^2)	\lim\:_{x\to\:0}(\frac{1-\cos(8x)}{4x^{2}})
(\partial)/(\partial x)(8x^{9y})	\frac{\partial\:}{\partial\:x}(8x^{9y})
integral of ((x^3-2sqrt(x))/x)	\int\:(\frac{x^{3}-2\sqrt{x}}{x})dx
derivative of (3x+6/(2sqrt(x+3)))	\frac{d}{dx}(\frac{3x+6}{2\sqrt{x+3}})
y^{''}+80y^'+1200y=0	y^{\prime\:\prime\:}+80y^{\prime\:}+1200y=0
integral of 2x(4x-3)^3	\int\:2x(4x-3)^{3}dx
derivative of 2/((3x^2+7)^2)	derivative\:\frac{2}{(3x^{2}+7)^{2}}
slope of f(x)=\sqrt[9]{x}	slope\:f(x)=\sqrt[9]{x}
integral of (sin(x))^3	\int\:(\sin(x))^{3}dx
(\partial)/(\partial r)(r)	\frac{\partial\:}{\partial\:r}(r)
integral of cos^2(5x)sin^3(5x)	\int\:\cos^{2}(5x)\sin^{3}(5x)dx
(\partial)/(\partial x)(x^{0.5}*y)	\frac{\partial\:}{\partial\:x}(x^{0.5}\cdot\:y)
limit as x approaches 0 of csc(x)	\lim\:_{x\to\:0}(\csc(x))
integral of x^2sqrt(4x+4)	\int\:x^{2}\sqrt{4x+4}dx
derivative of cos(3t)sin(2t)	derivative\:\cos(3t)\sin(2t)
integral of 6/(sin^2(x))	\int\:\frac{6}{\sin^{2}(x)}dx
derivative of f(x)=(x^3)/3+x^2+4x-10	derivative\:f(x)=\frac{x^{3}}{3}+x^{2}+4x-10
tangent of y=10x-x^2,(5,26)	tangent\:y=10x-x^{2},(5,26)
integral of 1/(xsqrt(-ln^2(x)+ln(x)+3))	\int\:\frac{1}{x\sqrt{-\ln^{2}(x)+\ln(x)+3}}dx
integral of (2x+5)/(sqrt(9-x^2))	\int\:\frac{2x+5}{\sqrt{9-x^{2}}}dx
derivative of y=sin(e^{2x})	derivative\:y=\sin(e^{2x})
derivative of (x+3/(8x^2e^x))	\frac{d}{dx}(\frac{x+3}{8x^{2}e^{x}})
limit as x approaches 0+of 2^x	\lim\:_{x\to\:0+}(2^{x})
derivative of (e^{x^2}+4^2(4x)^{3x})	\frac{d}{dx}((e^{x^{2}}+4)^{2}(4x)^{3x})
limit as x approaches 0+of x^{6sin(x)}	\lim\:_{x\to\:0+}(x^{6\sin(x)})
integral from 0 to pi/2 of (cos(t))/(sqrt(1+sin^2(t)))	\int\:_{0}^{\frac{π}{2}}\frac{\cos(t)}{\sqrt{1+\sin^{2}(t)}}dt
integral of (10)/(x^2sqrt(x^2+16))	\int\:\frac{10}{x^{2}\sqrt{x^{2}+16}}dx
integral of 1/(sqrt(x+2))	\int\:\frac{1}{\sqrt{x+2}}dx
limit as x approaches-3 of sqrt(-x+6)-3	\lim\:_{x\to\:-3}(\sqrt{-x+6}-3)
derivative of (3x^2+1)^2	derivative\:(3x^{2}+1)^{2}
(d^5)/(dx^5)(1/(x-1))	\frac{d^{5}}{dx^{5}}(\frac{1}{x-1})
integral of (-2sec^2(x))	\int\:(-2\sec^{2}(x))dx
derivative of y= 1/x+cos(2x)	derivative\:y=\frac{1}{x}+\cos(2x)
integral of 1/(sqrt(x)-\sqrt[4]{x)}	\int\:\frac{1}{\sqrt{x}-\sqrt[4]{x}}dx
integral from 0 to 1 of 6e^{2x}	\int\:_{0}^{1}6e^{2x}dx
integral of 1/(x(1+4x^2))	\int\:\frac{1}{x(1+4x^{2})}dx
simplify (-a)/(x^2)+a/((x-2)^2)	simplify\:\frac{-a}{x^{2}}+\frac{a}{(x-2)^{2}}
integral from 0 to 2 of 1/(4-2x)	\int\:_{0}^{2}\frac{1}{4-2x}dx
integral from 1 to 5 of (2+3x-x^2)	\int\:_{1}^{5}(2+3x-x^{2})dx
tangent of 1/(sqrt(10x))	tangent\:\frac{1}{\sqrt{10x}}
integral of 2e^{-t}	\int\:2e^{-t}dt
integral of 1/(x^2+2)	\int\:\frac{1}{x^{2}+2}dx
(dy)/(dx)=(x-2)/(y-4)	\frac{dy}{dx}=\frac{x-2}{y-4}
integral of x^3+sqrt(7x)-5xe^{-2x^2}	\int\:x^{3}+\sqrt{7x}-5xe^{-2x^{2}}dx
d/(dt)(tan(t))	\frac{d}{dt}(\tan(t))
limit as x approaches 3 of sqrt(x)-2	\lim\:_{x\to\:3}(\sqrt{x}-2)
(\partial)/(\partial x)(L-x*cos(b))	\frac{\partial\:}{\partial\:x}(L-x\cdot\:\cos(b))
integral of ycos(y)	\int\:y\cos(y)dy
slope of (-1/2 ,7),(1,-1)	slope\:(-\frac{1}{2},7),(1,-1)
e^{-y}cos(x)+(dy)/(dx)sin^2(x)=0	e^{-y}\cos(x)+\frac{dy}{dx}\sin^{2}(x)=0
derivative of (4x-3^{2x+1})	\frac{d}{dx}((4x-3)^{2x+1})
limit as x approaches-7 of (x^2-9)/(7-x)	\lim\:_{x\to\:-7}(\frac{x^{2}-9}{7-x})

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