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Popular Calculus Problems

integral from 2 to 8 of 1/(sqrt(2x)+1)	\int\:_{2}^{8}\frac{1}{\sqrt{2x}+1}dx
integral from 0 to 1 of 4t	\int\:_{0}^{1}4tdt
integral of 3x^2tan(y)-(2y^3)/(x^3)	\int\:3x^{2}\tan(y)-\frac{2y^{3}}{x^{3}}dx
integral of 1/((2x-3)^2+1)	\int\:\frac{1}{(2x-3)^{2}+1}dx
limit as x approaches 5 of 5	\lim\:_{x\to\:5}(5)
integral of ((3+sqrt(x))^2)/x	\int\:\frac{(3+\sqrt{x})^{2}}{x}dx
integral of 3xsqrt(2x+3)	\int\:3x\sqrt{2x+3}dx
integral of cos^3(x/8)	\int\:\cos^{3}(\frac{x}{8})dx
tangent of y= 1/(x^5),(3, 1/243)	tangent\:y=\frac{1}{x^{5}},(3,\frac{1}{243})
integral from-3 to 3 of 18-2x^2	\int\:_{-3}^{3}18-2x^{2}dx
limit as x approaches 2-of (3-x)/(2-x)	\lim\:_{x\to\:2-}(\frac{3-x}{2-x})
(xy+y^2+x^2)dx-x^2dy=0	(xy+y^{2}+x^{2})dx-x^{2}dy=0
limit as x approaches 0+of 1/(sqrt(x))	\lim\:_{x\to\:0+}(\frac{1}{\sqrt{x}})
limit as x approaches-4 of-(6/(x+4))	\lim\:_{x\to\:-4}(-(\frac{6}{x+4}))
integral of cos(ln(3x))	\int\:\cos(\ln(3x))dx
derivative of (x-a/(b-a))	\frac{d}{dx}(\frac{x-a}{b-a})
derivative of 5/(sqrt(x+9))	derivative\:\frac{5}{\sqrt{x+9}}
derivative of a(t-sin(t))	\frac{d}{dx}(a(t-\sin(t)))
derivative of ln(sin^3(x))	\frac{d}{dx}(\ln(\sin^{3}(x)))
integral from-4 to 12 of sqrt(z+4)	\int\:_{-4}^{12}\sqrt{z+4}dz
limit as x approaches 4 of x^2+sqrt(7-x)	\lim\:_{x\to\:4}(x^{2}+\sqrt{7-x})
x^2y^{''}-16xy^'+72y=0	x^{2}y^{\prime\:\prime\:}-16xy^{\prime\:}+72y=0
derivative of (sqrt(2)x/(x^2+1))	\frac{d}{dx}(\frac{\sqrt{2}x}{x^{2}+1})
derivative of f(x)=6x-x^2	derivative\:f(x)=6x-x^{2}
integral of 1/(5-5x)	\int\:\frac{1}{5-5x}dx
y^'+y^3x+y=0	y^{\prime\:}+y^{3}x+y=0
integral of cos(2u)	\int\:\cos(2u)du
integral from 0 to 2 of 3t^5	\int\:_{0}^{2}3t^{5}dt
derivative of xsqrt(5-x^2)	derivative\:x\sqrt{5-x^{2}}
f(x)=log_{8}(x)	f(x)=\log_{8}(x)
integral of k/(x^2)	\int\:\frac{k}{x^{2}}dx
y^{''}+0.1y^'+y=0	y^{\prime\:\prime\:}+0.1y^{\prime\:}+y=0
(\partial)/(\partial y)(9sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:y}(9\sqrt{x^{2}+y^{2}})
(5x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=2	(5x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(1)=2
(dy)/(dt)=2y-t^2	\frac{dy}{dt}=2y-t^{2}
integral from 0 to 2 of xsqrt(6-x^2)	\int\:_{0}^{2}x\sqrt{6-x^{2}}dx
integral of (x^2)/(4-x^3)	\int\:\frac{x^{2}}{4-x^{3}}dx
sum from x=1 to infinity of x/(x^2+1)	\sum\:_{x=1}^{\infty\:}\frac{x}{x^{2}+1}
integral from 0 to 7 of w^2ln(w)	\int\:_{0}^{7}w^{2}\ln(w)dw
integral of cot^3(t)	\int\:\cot^{3}(t)dt
tangent of y=-3cos(x),\at x=(-pi)/4	tangent\:y=-3\cos(x),\at\:x=\frac{-π}{4}
area sqrt(3x)+1,x+1	area\:\sqrt{3x}+1,x+1
integral of (sin^7(9x))/(cos^4(9x))	\int\:\frac{\sin^{7}(9x)}{\cos^{4}(9x)}dx
integral of x^3sqrt(x^2+4)	\int\:x^{3}\sqrt{x^{2}+4}dx
(dy)/(dx)-2xy=15x^2e^{x^2}	\frac{dy}{dx}-2xy=15x^{2}e^{x^{2}}
(\partial)/(\partial x)(xy(2+x)(y-3))	\frac{\partial\:}{\partial\:x}(xy(2+x)(y-3))
x^2(dy)/(dx)=y-xy,y(-1)=-5	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-5
derivative of 7e^x-((10/(x^4)))	\frac{d}{dx}(7e^{x}-(\frac{10}{x^{4}}))
derivative of f(x)=(2-1/x)/(x-3)	derivative\:f(x)=\frac{2-\frac{1}{x}}{x-3}
limit as x approaches-2-of g(x)	\lim\:_{x\to\:-2-}(g(x))
limit as x approaches 0 of (1+x/3)^{1/x}	\lim\:_{x\to\:0}((1+\frac{x}{3})^{\frac{1}{x}})
integral of (θ^4+sec^2(θ))	\int\:(θ^{4}+\sec^{2}(θ))dθ
area y=sin(2)(x),y=sin(3)(x),0<= x<= pi	area\:y=\sin(2)(x),y=\sin(3)(x),0\le\:x\le\:π
derivative of sqrt(x)-1/(sqrt(x))	derivative\:\sqrt{x}-\frac{1}{\sqrt{x}}
laplacetransform te^{-t}sin(2t)	laplacetransform\:te^{-t}\sin(2t)
y^'-4/t y=t^5e^t	y^{\prime\:}-\frac{4}{t}y=t^{5}e^{t}
limit as x approaches 1-of (x-3)/(x-1)	\lim\:_{x\to\:1-}(\frac{x-3}{x-1})
integral of y(2y+1)e^{4y^3+3y^2-4}	\int\:y(2y+1)e^{4y^{3}+3y^{2}-4}dy
factor 5x^2-x^3	factor\:5x^{2}-x^{3}
integral of (5-2/3 x^2+3/4 x^3)	\int\:(5-\frac{2}{3}x^{2}+\frac{3}{4}x^{3})dx
x(dy)/(dx)+2y=5x^3	x\frac{dy}{dx}+2y=5x^{3}
integral of (39)/(39+e^x)	\int\:\frac{39}{39+e^{x}}dx
limit as x approaches-2 of 5x+2	\lim\:_{x\to\:-2}(5x+2)
tangent of y=sqrt(x)	tangent\:y=\sqrt{x}
y^{''}-2y^'+y=14.5e^t	y^{\prime\:\prime\:}-2y^{\prime\:}+y=14.5e^{t}
integral of (1-y^2)^{-1/2}	\int\:(1-y^{2})^{-\frac{1}{2}}dy
y^'+y/x =9x^3y^2	y^{\prime\:}+\frac{y}{x}=9x^{3}y^{2}
derivative of n^x	\frac{d}{dx}(n^{x})
y^{''}+6y^'+9y=0	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=0
(dy)/(dt)-(3/t)y=2t^3e^{2t},y(1)=0	\frac{dy}{dt}-(\frac{3}{t})y=2t^{3}e^{2t},y(1)=0
integral of (x+5)/(x-2)	\int\:\frac{x+5}{x-2}dx
integral of 6θcos(θ)	\int\:6θ\cos(θ)dθ
derivative of (x+2)/(4x-3)	derivative\:\frac{x+2}{4x-3}
integral of x/((x^2-2x+5))	\int\:\frac{x}{(x^{2}-2x+5)}dx
y^'=y^2-3y	y^{\prime\:}=y^{2}-3y
integral of x(2x+5)^8	\int\:x(2x+5)^{8}dx
integral of e^xsqrt(4-e^{2x)}	\int\:e^{x}\sqrt{4-e^{2x}}dx
derivative of ln(sin(t))	derivative\:\ln(\sin(t))
integral of (xcos(x))/(sin^2(x))	\int\:\frac{x\cos(x)}{\sin^{2}(x)}dx
(\partial)/(\partial x)((x+10)^2*(y+2))	\frac{\partial\:}{\partial\:x}((x+10)^{2}\cdot\:(y+2))
derivative of f(x)=(x^3)/3+3/(x^3)	derivative\:f(x)=\frac{x^{3}}{3}+\frac{3}{x^{3}}
integral of x5^{-x}	\int\:x5^{-x}dx
integral of x(2x+5)	\int\:x(2x+5)dx
(\partial)/(\partial x)(8e^{xy})	\frac{\partial\:}{\partial\:x}(8e^{xy})
(dy)/(dt)=-y^2	\frac{dy}{dt}=-y^{2}
derivative of 5xln(3x)-5x	derivative\:5x\ln(3x)-5x
(df)/(dx)x=x^3	\frac{df}{dx}x=x^{3}
integral of 1/(\sqrt[7]{x^2)}	\int\:\frac{1}{\sqrt[7]{x^{2}}}dx
integral of ((2x^2-1))/(x-x^3)	\int\:\frac{(2x^{2}-1)}{x-x^{3}}dx
derivative of sin(tan(x^5))	\frac{d}{dx}(\sin(\tan(x^{5})))
integral of (11x^3-1)/(\sqrt[3]{x)}	\int\:\frac{11x^{3}-1}{\sqrt[3]{x}}dx
(dy)/(dx)=3-0.0003y	\frac{dy}{dx}=3-0.0003y
derivative of 3x^2-6x+5	\frac{d}{dx}(3x^{2}-6x+5)
integral of (1/y-1)	\int\:(\frac{1}{y}-1)dy
y^{''}+4y^'+6y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=0,y(0)=1,y^{\prime\:}(0)=0
y^'=x+y,y(0)=9	y^{\prime\:}=x+y,y(0)=9
derivative of x+1-tan(x/4)	\frac{d}{dx}(x+1-\tan(\frac{x}{4}))
limit as x approaches 6-of 1/(x-6)	\lim\:_{x\to\:6-}(\frac{1}{x-6})
integral of 9/((x-4)(x+2))	\int\:\frac{9}{(x-4)(x+2)}dx
integral of t^4e^{t^5}	\int\:t^{4}e^{t^{5}}dt

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