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Popular Calculus Problems

derivative of 2x(1-x^3-3x^2(1-x)^2)	\frac{d}{dx}(2x(1-x)^{3}-3x^{2}(1-x)^{2})
integral of (x+1)/(x+2)	\int\:\frac{x+1}{x+2}dx
integral of x/(sqrt(x+20))	\int\:\frac{x}{\sqrt{x+20}}dx
(sqrt(x)+x)((dy)/(dx))=sqrt(y)+y	(\sqrt{x}+x)(\frac{dy}{dx})=\sqrt{y}+y
tangent of f(x)=cos(x),\at (0)	tangent\:f(x)=\cos(x),\at\:(0)
derivative of y=((2x+1)(x^3+3))/x	derivative\:y=\frac{(2x+1)(x^{3}+3)}{x}
tangent of 4x^2-2x+3	tangent\:4x^{2}-2x+3
integral from 0 to pi of sin(x)+cos(2x)	\int\:_{0}^{π}\sin(x)+\cos(2x)dx
y^'+4/5 y=1-1/4 t,y(0)=0	y^{\prime\:}+\frac{4}{5}y=1-\frac{1}{4}t,y(0)=0
integral of (e^{2x})/(sqrt(1-e^x))	\int\:\frac{e^{2x}}{\sqrt{1-e^{x}}}dx
derivative of-sqrt(1-x)	\frac{d}{dx}(-\sqrt{1-x})
integral from 0 to 1/6 of xarcsin(6x)	\int\:_{0}^{\frac{1}{6}}x\arcsin(6x)dx
integral of (cos(x)-sin(2x))	\int\:(\cos(x)-\sin(2x))dx
(dy)/(dx)+2y=35sin(x)+15cos(x),y(0)=9	\frac{dy}{dx}+2y=35\sin(x)+15\cos(x),y(0)=9
(\partial)/(\partial y)(e^{-x}sec(y))	\frac{\partial\:}{\partial\:y}(e^{-x}\sec(y))
derivative of sqrt(x^4+x)	\frac{d}{dx}(\sqrt{x^{4}+x})
derivative of sin^2(2x)	\frac{d}{dx}(\sin^{2}(2x))
integral of (\sqrt[3]{x}+\sqrt[4]{x})	\int\:(\sqrt[3]{x}+\sqrt[4]{x})dx
derivative of y=-x^2+62	derivative\:y=-x^{2}+62
derivative of (cos(x)/(cos(x)+1))	\frac{d}{dx}(\frac{\cos(x)}{\cos(x)+1})
simplify (x^2+x+1)/(2sqrt(x))	simplify\:\frac{x^{2}+x+1}{2\sqrt{x}}
integral of (8x)/(8x+3)	\int\:\frac{8x}{8x+3}dx
derivative of (7-3x^3^2)	\frac{d}{dx}((7-3x^{3})^{2})
integral from 0 to 2 of xe^{-x}	\int\:_{0}^{2}xe^{-x}dx
limit as x approaches 0 of (x-2)e^{-1/x}	\lim\:_{x\to\:0}((x-2)e^{-\frac{1}{x}})
x((dy)/(dx))=2x+2y	x(\frac{dy}{dx})=2x+2y
integral of 1/(1+29x)	\int\:\frac{1}{1+29x}dx
limit as x approaches 0 of-3/x	\lim\:_{x\to\:0}(-\frac{3}{x})
derivative of-(20,0)/(sqrt(1+0.2t))+21,0	derivative\:-\frac{20,0}{\sqrt{1+0.2t}}+21,0
integral of x^8ln(x)	\int\:x^{8}\ln(x)dx
integral from 0 to pi/2 of sin^6(x)	\int\:_{0}^{\frac{π}{2}}\sin^{6}(x)dx
integral of (2+sqrt(x))/(2-sqrt(x))	\int\:\frac{2+\sqrt{x}}{2-\sqrt{x}}dx
integral from-2 to 9 of 7/((4x-3)^2)	\int\:_{-2}^{9}\frac{7}{(4x-3)^{2}}dx
integral of 24y(x-yx-(x^2)/2)	\int\:24y(x-yx-\frac{x^{2}}{2})dy
integral of x(x+3)	\int\:x(x+3)dx
tangent of 2xe^x	tangent\:2xe^{x}
integral of 2te^{-t^2}	\int\:2te^{-t^{2}}dt
integral from 0 to 1 of xsqrt(1-x^2)	\int\:_{0}^{1}x\sqrt{1-x^{2}}dx
integral of (2u-1)/(-u+2)	\int\:\frac{2u-1}{-u+2}du
derivative of ((x+1^2)/(x+3))	\frac{d}{dx}(\frac{(x+1)^{2}}{x+3})
derivative of e^{1/3 x}	\frac{d}{dx}(e^{\frac{1}{3}x})
derivative of e^{-x}-e^{-x}x	derivative\:e^{-x}-e^{-x}x
derivative of e^{x-4}	\frac{d}{dx}(e^{x-4})
(dy)/(dx)=(1+y^2)tan(x),y(0)=1	\frac{dy}{dx}=(1+y^{2})\tan(x),y(0)=1
limit as x approaches 1 of sqrt(2x)	\lim\:_{x\to\:1}(\sqrt{2x})
tangent of f(x)=x^2-2x,(5,9)	tangent\:f(x)=x^{2}-2x,(5,9)
limit as x approaches 0 of (1+x-1)/x	\lim\:_{x\to\:0}(\frac{1+x-1}{x})
integral from 0 to 3 of c*(3-x)	\int\:_{0}^{3}c\cdot\:(3-x)dx
slope of (1,-2),(3,4)	slope\:(1,-2),(3,4)
limit as x approaches 0 of sqrt(x-6)	\lim\:_{x\to\:0}(\sqrt{x-6})
derivative of cos(x^3+5x)	\frac{d}{dx}(\cos(x^{3}+5x))
derivative of 1/(3(1+x)^{2/3)}	derivative\:\frac{1}{3(1+x)^{\frac{2}{3}}}
laplacetransform t^2	laplacetransform\:t^{2}
(\partial)/(\partial x)((x^2+y^2)^{-1/2})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{-\frac{1}{2}})
derivative of 1+e^{0.5499-0.09x}	derivative\:1+e^{0.5499-0.09x}
derivative of y=cos(ln(4x^3))	derivative\:y=\cos(\ln(4x^{3}))
derivative of y=e^xsin(x)+cos(x)e^x	derivative\:y=e^{x}\sin(x)+\cos(x)e^{x}
derivative of f(x)=((6x^2-6x+6)^5)	derivative\:f(x)=((6x^{2}-6x+6)^{5})
derivative of 3x^3ln(x^2)	derivative\:3x^{3}\ln(x^{2})
sum from n=0 to infinity of 0	\sum\:_{n=0}^{\infty\:}0
integral of sqrt(x)+x^2	\int\:\sqrt{x}+x^{2}dx
tangent of y=5x^4+3x-6,(1,2)	tangent\:y=5x^{4}+3x-6,(1,2)
(\partial)/(\partial y)((5xy)/(10x-y))	\frac{\partial\:}{\partial\:y}(\frac{5xy}{10x-y})
integral from-8 to 8 of (64-x^2)	\int\:_{-8}^{8}(64-x^{2})dx
inverse oflaplace 2/((s+3))	inverselaplace\:\frac{2}{(s+3)}
derivative of 1/(sin(3x))	\frac{d}{dx}(\frac{1}{\sin(3x)})
derivative of (x^2+2x-6/((x+1)^2))	\frac{d}{dx}(\frac{x^{2}+2x-6}{(x+1)^{2}})
(x^2+1)y^{''}-2xy^'+2y=0	(x^{2}+1)y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=0
tangent of f(x)=6e^x+x,(0,6)	tangent\:f(x)=6e^{x}+x,(0,6)
derivative of cos^4(2x^3-5)	\frac{d}{dx}(\cos^{4}(2x^{3}-5))
integral of (5-2x^2)/(y^2)	\int\:\frac{5-2x^{2}}{y^{2}}dy
integral of sin(10x)	\int\:\sin(10x)dx
area y=x(x+3)(x-4),x=0	area\:y=x(x+3)(x-4),x=0
(5e^x)^'	(5e^{x})^{\prime\:}
limit as x approaches 0 of 1/(tan(x))	\lim\:_{x\to\:0}(\frac{1}{\tan(x)})
integral from b to 2b of x^8	\int\:_{b}^{2b}x^{8}dx
derivative of sec^2(x-2)	\frac{d}{dx}(\sec^{2}(x)-2)
integral of x(x-2)^4	\int\:x(x-2)^{4}dx
sum from n=1 to infinity of 1/(n^2+300)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+300}
y^'=2y(5-y)	y^{\prime\:}=2y(5-y)
tangent of f(x)=(x^2-2)(x^3-3x),\at x=-2	tangent\:f(x)=(x^{2}-2)(x^{3}-3x),\at\:x=-2
limit as x approaches 0 of (x^2-5)/(x-2)	\lim\:_{x\to\:0}(\frac{x^{2}-5}{x-2})
(d^2)/(dx^2)xy+2x^2=5	\frac{d^{2}}{dx^{2}}xy+2x^{2}=5
integral of sin^3(x)*cos(x)	\int\:\sin^{3}(x)\cdot\:\cos(x)dx
(\partial)/(\partial x)(\sqrt[4]{6x^2+4})	\frac{\partial\:}{\partial\:x}(\sqrt[4]{6x^{2}+4})
derivative of 7/(sqrt(x+4))	derivative\:\frac{7}{\sqrt{x+4}}
integral of x^3e^{x^4+5}	\int\:x^{3}e^{x^{4}+5}dx
y+y^4=(y^6+3x)y^'	y+y^{4}=(y^{6}+3x)y^{\prime\:}
cos(x)y^'-sin(x)y=0	\cos(x)y^{\prime\:}-\sin(x)y=0
integral of (9x)/(\sqrt[4]{x+2)}	\int\:\frac{9x}{\sqrt[4]{x+2}}dx
integral of (3-z)/(-1+z^2)	\int\:\frac{3-z}{-1+z^{2}}dz
derivative of cos(sin(5)x^3)	derivative\:\cos(\sin(5)x^{3})
derivative of ln(x/a)	\frac{d}{dx}(\ln(\frac{x}{a}))
integral of (8+t+t^2)/(sqrt(t))	\int\:\frac{8+t+t^{2}}{\sqrt{t}}dt
integral of e^{sqrt(3x)}	\int\:e^{\sqrt{3x}}dx
tangent of 8x^2+3x	tangent\:8x^{2}+3x
derivative of sqrt(2cx+c^2)	\frac{d}{dx}(\sqrt{2cx+c^{2}})
derivative of f(x)=2x^2-x^3	derivative\:f(x)=2x^{2}-x^{3}
derivative of (2t-1)(4t-6)^{-1}	derivative\:(2t-1)(4t-6)^{-1}
x^2y^{''}-2y=0,y(1)=0,y^'(1)=3	x^{2}y^{\prime\:\prime\:}-2y=0,y(1)=0,y^{\prime\:}(1)=3

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