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Popular Calculus Problems

integral from 0 to pi/4 of cos^2(4x)	\int\:_{0}^{\frac{π}{4}}\cos^{2}(4x)dx
integral of (2x+1)/(x^3-7x+6)	\int\:\frac{2x+1}{x^{3}-7x+6}dx
derivative of 1300+14x-0.1x^2+0.0005x^3	derivative\:1300+14x-0.1x^{2}+0.0005x^{3}
(\partial)/(\partial x)(4(e^x-x^2y))	\frac{\partial\:}{\partial\:x}(4(e^{x}-x^{2}y))
derivative of (20x+x^2/((10+x)^2))	\frac{d}{dx}(\frac{20x+x^{2}}{(10+x)^{2}})
integral of 1/(cos^2(y))	\int\:\frac{1}{\cos^{2}(y)}dy
derivative of 2x^5-3e^{6x}	derivative\:2x^{5}-3e^{6x}
integral of (12)/(1-cos(6x))	\int\:\frac{12}{1-\cos(6x)}dx
derivative of 3x^2(2x+1^5)	\frac{d}{dx}(3x^{2}(2x+1)^{5})
derivative of-0.251(x-3.58)^2+3.3	derivative\:-0.251(x-3.58)^{2}+3.3
derivative of 0.2x	\frac{d}{dx}(0.2x)
integral of ((4x))/(x^2+3)	\int\:\frac{(4x)}{x^{2}+3}dx
sqrt(x+2), 1/(x+1),x=2,x=0	\sqrt{x+2},\frac{1}{x+1},x=2,x=0
derivative of 6e^x+2/(\sqrt[3]{x)}	derivative\:6e^{x}+\frac{2}{\sqrt[3]{x}}
integral of 1/((1-x)^6)	\int\:\frac{1}{(1-x)^{6}}dx
tangent of (-8x)/(x^2+1)(0)	tangent\:\frac{-8x}{x^{2}+1}(0)
integral of sec^2(3x)	\int\:\sec^{2}(3x)dx
integral of cos^2(4t)	\int\:\cos^{2}(4t)dt
taylor x^{-2},5	taylor\:x^{-2},5
derivative of sin(x^{12})	\frac{d}{dx}(\sin(x^{12}))
limit as x approaches 0 of (-1)/x	\lim\:_{x\to\:0}(\frac{-1}{x})
parity x^2sin(x)tan(x)	parity\:x^{2}\sin(x)\tan(x)
derivative of 5sin(2x)	derivative\:5\sin(2x)
derivative of e^xx-2e^x	\frac{d}{dx}(e^{x}x-2e^{x})
derivative of ln(20)	derivative\:\ln(20)
integral from y to 1 of 8xy	\int\:_{y}^{1}8xydx
derivative of (2xy/((x^2+y^2)^2))	\frac{d}{dx}(\frac{2xy}{(x^{2}+y^{2})^{2}})
derivative of 1/(5x^8)	\frac{d}{dx}(\frac{1}{5x^{8}})
limit as n approaches infinity of n^{-1}	\lim\:_{n\to\:\infty\:}(n^{-1})
derivative of f(x)=ln\|cot(3*x)\|	derivative\:f(x)=\ln\left\|\cot(3\cdot\:x)\right\|
((3x^2+3x+4)^'(3x^2+6x)^')^'	((3x^{2}+3x+4)^{\prime\:}(3x^{2}+6x)^{\prime\:})^{\prime\:}
integral of e^{tan(2x)}sec^2(2x)	\int\:e^{\tan(2x)}\sec^{2}(2x)dx
integral of 1/(3x^4)	\int\:\frac{1}{3x^{4}}dx
integral from-1 to 1 of 1/2 (4-4x^2)^2	\int\:_{-1}^{1}\frac{1}{2}(4-4x^{2})^{2}dx
(\partial}{\partial t}(\frac{s-3r)/t)	\frac{\partial\:}{\partial\:t}(\frac{s-3r}{t})
y^{''}-y=x	y^{\prime\:\prime\:}-y=x
derivative of 7/(3x^4)	\frac{d}{dx}(\frac{7}{3x^{4}})
limit as x approaches 8 of (x-8)/x	\lim\:_{x\to\:8}(\frac{x-8}{x})
limit as x approaches infinity of (6x^2)/(e^{5x)}	\lim\:_{x\to\:\infty\:}(\frac{6x^{2}}{e^{5x}})
(\partial)/(\partial x)(ln\|xy\|)	\frac{\partial\:}{\partial\:x}(\ln\left\|xy\right\|)
limit as x approaches-2 of (x^2+2)/(x-2)	\lim\:_{x\to\:-2}(\frac{x^{2}+2}{x-2})
integral of e^{x/a}	\int\:e^{\frac{x}{a}}dx
integral of 1/(xsqrt(x+9))	\int\:\frac{1}{x\sqrt{x+9}}dx
y^{''}+10y^'+25y=0	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=0
(\partial)/(\partial x)(1,1,-2)	\frac{\partial\:}{\partial\:x}(1,1,-2)
slope ofintercept (-4)(0.2)	slopeintercept\:(-4)(0.2)
integral of sec^8(2x)tan(2x)	\int\:\sec^{8}(2x)\tan(2x)dx
slope of (2.4)(6.6)	slope\:(2.4)(6.6)
derivative of 2x^3y	\frac{d}{dx}(2x^{3}y)
integral of 1/(sqrt(x-3))	\int\:\frac{1}{\sqrt{x-3}}dx
area y=12-x,y=sqrt(x),y=1	area\:y=12-x,y=\sqrt{x},y=1
derivative of e^tcos(6t)	derivative\:e^{t}\cos(6t)
integral from-3 to 1 of 2e^x	\int\:_{-3}^{1}2e^{x}dx
derivative of y=x^4+3e^x	derivative\:y=x^{4}+3e^{x}
derivative of tan(sqrt(x)+1)	derivative\:\tan(\sqrt{x}+1)
derivative of ln(3+x)	\frac{d}{dx}(\ln(3+x))
derivative of (3sqrt(x)+4x^2)	\frac{d}{dx}((3\sqrt{x}+4)x^{2})
integral of 1/(n^2+1)	\int\:\frac{1}{n^{2}+1}
integral of xcos(xy)	\int\:x\cos(xy)dy
derivative of ln(4x^2+1)	\frac{d}{dx}(\ln(4x^{2}+1))
derivative of 1000(1-e^{-0.15x})	\frac{d}{dx}(1000(1-e^{-0.15x}))
derivative of 3^xlog_{3}(x)	derivative\:3^{x}\log_{3}(x)
area 9-x^2,-8x	area\:9-x^{2},-8x
derivative of x/(x+5)	\frac{d}{dx}(\frac{x}{x+5})
(dy)/(dx)=x(4-y)	\frac{dy}{dx}=x(4-y)
sum from n=0 to infinity of n(3/5)^n	\sum\:_{n=0}^{\infty\:}n(\frac{3}{5})^{n}
25x^2y^{''}+25xy^'+y=0	25x^{2}y^{\prime\:\prime\:}+25xy^{\prime\:}+y=0
limit as x approaches infinity of x^x	\lim\:_{x\to\:\infty\:}(x^{x})
derivative of (-8x-2)/(9x-4)	derivative\:\frac{-8x-2}{9x-4}
(\partial)/(\partial x)(4x^3+y)	\frac{\partial\:}{\partial\:x}(4x^{3}+y)
derivative of (10x+1)/(x+100)	derivative\:\frac{10x+1}{x+100}
derivative of 7^{x^7}	derivative\:7^{x^{7}}
limit as x approaches-1 of-sqrt(x^2+3)	\lim\:_{x\to\:-1}(-\sqrt{x^{2}+3})
(dy)/(dt)-3y=te^{2t}	\frac{dy}{dt}-3y=te^{2t}
(\partial)/(\partial y)(x^3-2xy+15)	\frac{\partial\:}{\partial\:y}(x^{3}-2xy+15)
integral of 1/(e^{-v)+1}	\int\:\frac{1}{e^{-v}+1}dv
integral of x^3*sin(2x)	\int\:x^{3}\cdot\:\sin(2x)dx
inverse oflaplace (3s)/((s-1)(s^2+1))	inverselaplace\:\frac{3s}{(s-1)(s^{2}+1)}
limit as x approaches infinity of 2x-2	\lim\:_{x\to\:\infty\:}(2x-2)
inverse oflaplace 1/(4s+1)	inverselaplace\:\frac{1}{4s+1}
y^'+2y=6,y(0)=0	y^{\prime\:}+2y=6,y(0)=0
slope of (2.5)(1.1)	slope\:(2.5)(1.1)
integral of ((x^2+x+1))/((x^2+1)^2)	\int\:\frac{(x^{2}+x+1)}{(x^{2}+1)^{2}}dx
integral from a to x of 1/(b-a)	\int\:_{a}^{x}\frac{1}{b-a}dx
derivative of (cos(2x+x^3)/(tan(2x)-3x))	\frac{d}{dx}(\frac{\cos(2x)+x^{3}}{\tan(2x)-3x})
limit as x approaches 2-of (x+5)/(x-2)	\lim\:_{x\to\:2-}(\frac{x+5}{x-2})
inverse oflaplace-(e^{-pis})/(s^2+1)	inverselaplace\:-\frac{e^{-πs}}{s^{2}+1}
slope of (1950,38300),(2000,82500)	slope\:(1950,38300),(2000,82500)
f^'(x)=x^2-5	f^{\prime\:}(x)=x^{2}-5
integral of 1/(3x^2+6x+78)	\int\:\frac{1}{3x^{2}+6x+78}dx
integral of e^{4x}cos(7x)	\int\:e^{4x}\cos(7x)dx
t^2(dy)/(dt)+y=0,y(6)=-3,t>0	t^{2}\frac{dy}{dt}+y=0,y(6)=-3,t>0
integral of cos(3x^2+5)x	\int\:\cos(3x^{2}+5)xdx
derivative of sqrt(10000-40x-0.02x^2)	\frac{d}{dx}(\sqrt{10000-40x-0.02x^{2}})
integral of (3x^2+14x+13)/(x+4)	\int\:\frac{3x^{2}+14x+13}{x+4}dx
integral of 1/((xsqrt(x-1)))	\int\:\frac{1}{(x\sqrt{x-1})}dx
integral of (x^2-14x-5)/((x-1)^2(x^2+1))	\int\:\frac{x^{2}-14x-5}{(x-1)^{2}(x^{2}+1)}dx
derivative of f(x)=sqrt(9x+5)	derivative\:f(x)=\sqrt{9x+5}
integral of sqrt(r^2-x^2)	\int\:\sqrt{r^{2}-x^{2}}dx
(dy)/(dx)=6-x	\frac{dy}{dx}=6-x

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