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Popular Calculus Problems

integral of x/(sqrt(x-10))	\int\:\frac{x}{\sqrt{x-10}}dx
sum from n=1 to infinity of \sqrt[n]{2}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{2}
y^'-2=2y^2	y^{\prime\:}-2=2y^{2}
slope of (4,0),(0,-1)	slope\:(4,0),(0,-1)
derivative of (5+6x/(9-4x))	\frac{d}{dx}(\frac{5+6x}{9-4x})
derivative of f(1)=x+1/x	derivative\:f(1)=x+\frac{1}{x}
derivative of x/((x^2+1^2))	\frac{d}{dx}(\frac{x}{(x^{2}+1)^{2}})
integral of (12)/(1+4x^2)	\int\:\frac{12}{1+4x^{2}}dx
derivative of \sqrt[3]{x^{9.6}}+2e^{1.3}	\frac{d}{dx}(\sqrt[3]{x^{9.6}}+2e^{1.3})
integral from 1 to 2 of (1/t-i)^2	\int\:_{1}^{2}(\frac{1}{t}-i)^{2}dt
y^'=ay-by^2	y^{\prime\:}=ay-by^{2}
derivative of (x^8/(16))	\frac{d}{dx}(\frac{x^{8}}{16})
limit as x approaches 1+of (x+2)/(x+1)	\lim\:_{x\to\:1+}(\frac{x+2}{x+1})
integral from 1 to 3 of 1/(sqrt(x)(x+1))	\int\:_{1}^{3}\frac{1}{\sqrt{x}(x+1)}dx
integral from 1 to x^2 of sin^2(t)	\int\:_{1}^{x^{2}}\sin^{2}(t)dt
(\partial)/(\partial x)((x+3y)^3)	\frac{\partial\:}{\partial\:x}((x+3y)^{3})
derivative of (a+b/(x^2))^3	derivative\:(a+\frac{b}{x^{2}})^{3}
f(x)=e^{4x}+4e^{4x}x	f(x)=e^{4x}+4e^{4x}x
limit as x approaches infinity of (ln^3(x))/(100\sqrt[3]{x)}	\lim\:_{x\to\:\infty\:}(\frac{\ln^{3}(x)}{100\sqrt[3]{x}})
integral of 12xe^{-3x}	\int\:12xe^{-3x}dx
derivative of xcox(x)	\frac{d}{dx}(xcox(x))
tangent of f(x)=2+1/x ,(4,2.25)	tangent\:f(x)=2+\frac{1}{x},(4,2.25)
integral from-2 to 2 of (x^3-2x+3)	\int\:_{-2}^{2}(x^{3}-2x+3)dx
integral of (6x^2y-2x)	\int\:(6x^{2}y-2x)dy
integral from 0 to 1 of-9(x^2+1)e^{-x}	\int\:_{0}^{1}-9(x^{2}+1)e^{-x}dx
tangent of y=(1+2x)^2,(1,9)	tangent\:y=(1+2x)^{2},(1,9)
(\partial)/(\partial x)(arctan(yx))	\frac{\partial\:}{\partial\:x}(\arctan(yx))
derivative of 1+x	\frac{d}{dx}(1+x)
xy^'-y=x^2	xy^{\prime\:}-y=x^{2}
limit as x approaches 7 of sqrt(x-7)	\lim\:_{x\to\:7}(\sqrt{x-7})
integral of+((x^2))/2	\int\:+\frac{(x^{2})}{2}dx
derivative of (x^2+sec(x)/(x-2e^x))	\frac{d}{dx}(\frac{x^{2}+\sec(x)}{x-2e^{x}})
integral of-e^{-x}2x	\int\:-e^{-x}2xdx
derivative of y=2t(3t^2-5)^3	derivative\:y=2t(3t^{2}-5)^{3}
derivative of e^x(x^2+5x)	\frac{d}{dx}(e^{x}(x^{2}+5x))
derivative of xsqrt(3x-2)	\frac{d}{dx}(x\sqrt{3x-2})
xy^'+y=0,y(4)=6	xy^{\prime\:}+y=0,y(4)=6
derivative of f(x)= 4/x-2/(x^3)+1/(x^4)	derivative\:f(x)=\frac{4}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}}
tangent of y=-7/2 x^2+5x+5,(-1,-7/2)	tangent\:y=-\frac{7}{2}x^{2}+5x+5,(-1,-\frac{7}{2})
integral of cos^3(x)sin^{-4}(x)	\int\:\cos^{3}(x)\sin^{-4}(x)dx
(dy)/(dx)=((x^3))/(y^2)	\frac{dy}{dx}=\frac{(x^{3})}{y^{2}}
integral of (4e^x-x^3+6x-8)	\int\:(4e^{x}-x^{3}+6x-8)dx
sum from n=0 to infinity of 1/(4n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{4n+1}
integral of 1/(e^x)	\int\:\frac{1}{e^{x}}dx
y^{''}+4y^'+2y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+2y=0
(\partial)/(\partial u)(tan(u/v))	\frac{\partial\:}{\partial\:u}(\tan(\frac{u}{v}))
integral of x/((3x^2-4)^2)	\int\:\frac{x}{(3x^{2}-4)^{2}}dx
area 4x^2,16	area\:4x^{2},16
derivative of f(x)=sqrt(7x^4+5)	derivative\:f(x)=\sqrt{7x^{4}+5}
(\partial)/(\partial y)(sqrt(4-x^2-9y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-9y^{2}})
integral of 4xye^{-(2x+y)}	\int\:4xye^{-(2x+y)}dy
y^'=6x-y	y^{\prime\:}=6x-y
integral from 0 to 0.1 of kx	\int\:_{0}^{0.1}kxdx
(\partial)/(\partial x)(arctan(xsqrt(y)))	\frac{\partial\:}{\partial\:x}(\arctan(x\sqrt{y}))
integral of 2cos^2(x)	\int\:2\cos^{2}(x)dx
derivative of sqrt(cos(e^{x^2cos(x))})	\frac{d}{dx}(\sqrt{\cos(e^{x^{2}\cos(x)})})
sum from n=1 to infinity of (4^n)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{4^{n}}{5^{n}}
derivative of sqrt(8t^2-t)	derivative\:\sqrt{8t^{2}-t}
derivative of (3x+5)^2	derivative\:(3x+5)^{2}
(2x-1)dx+(7y+8)dy=0	(2x-1)dx+(7y+8)dy=0
limit as x approaches-5 of 4	\lim\:_{x\to\:-5}(4)
integral of ((1+sqrt(x))^9)/(sqrt(x))	\int\:\frac{(1+\sqrt{x})^{9}}{\sqrt{x}}dx
integral of 1/(xsqrt(361x^2-361))	\int\:\frac{1}{x\sqrt{361x^{2}-361}}dx
tangent of f(x)=16sqrt(x),(16,64)	tangent\:f(x)=16\sqrt{x},(16,64)
integral of 1/(1-3x)	\int\:\frac{1}{1-3x}dx
derivative of f(t)=(5t^2+t+6)/(sqrt(t))	derivative\:f(t)=\frac{5t^{2}+t+6}{\sqrt{t}}
integral of (7x)/((1-x^2)^3)	\int\:\frac{7x}{(1-x^{2})^{3}}dx
limit as x approaches pi of (cos(x))/x	\lim\:_{x\to\:π}(\frac{\cos(x)}{x})
y^'=2xy+3y-4x-6	y^{\prime\:}=2xy+3y-4x-6
limit as x approaches infinity of-e^x	\lim\:_{x\to\:\infty\:}(-e^{x})
integral of e^{2x}sqrt(1-4e^{2x)}	\int\:e^{2x}\sqrt{1-4e^{2x}}dx
integral of 2sin^3(3x)cos^3(3x)	\int\:2\sin^{3}(3x)\cos^{3}(3x)dx
limit as x approaches infinity of (4x-5)/(2x+3)	\lim\:_{x\to\:\infty\:}(\frac{4x-5}{2x+3})
sum from n=1 to infinity of (4n)/(4n+7)	\sum\:_{n=1}^{\infty\:}\frac{4n}{4n+7}
derivative of (2x+5)(4x-5)^2	derivative\:(2x+5)(4x-5)^{2}
derivative of ln(x^{sin(x}))	\frac{d}{dx}(\ln(x^{\sin(x)}))
integral of 1/(xsqrt(9x-1))	\int\:\frac{1}{x\sqrt{9x-1}}dx
integral of ((cos(x))/(sin(2x)))	\int\:(\frac{\cos(x)}{\sin(2x)})dx
derivative of (x+1770)/(30(x+2))	derivative\:\frac{x+1770}{30(x+2)}
derivative of 2x(3x-2^4)	\frac{d}{dx}(2x(3x-2)^{4})
integral of (t^5)/(t^6+1)	\int\:\frac{t^{5}}{t^{6}+1}dt
sum from n=1 to infinity of 2/(4^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{2}{4^{2n}}
limit as h approaches 0 of ((7/(x+h)-7/x))/h	\lim\:_{h\to\:0}(\frac{(\frac{7}{x+h}-\frac{7}{x})}{h})
limit as x approaches 1 of ln\|x-1\|	\lim\:_{x\to\:1}(\ln\left\|x-1\right\|)
(\partial ^2)/(\partial x^2)(2cos(xy^2))	\frac{\partial\:^{2}}{\partial\:x^{2}}(2\cos(xy^{2}))
((dy)/(dx))=(x+y+7)^2	(\frac{dy}{dx})=(x+y+7)^{2}
-(xsqrt(1-y^2))/(ysqrt(1-x^2))=(dy)/(dx)	-\frac{x\sqrt{1-y^{2}}}{y\sqrt{1-x^{2}}}=\frac{dy}{dx}
sum from n=0 to infinity of (n^2+1)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}+1}{n!}
d/(du)(sqrt((u-1)/(u+1)))	\frac{d}{du}(\sqrt{\frac{u-1}{u+1}})
(d^2y)/(dx^2)-(dy)/(dx)-30y=0	\frac{d^{2}y}{dx^{2}}-\frac{dy}{dx}-30y=0
derivative of sin^3(cos(7x^2))	\frac{d}{dx}(\sin^{3}(\cos(7x^{2})))
(dy)/(dt)-2y=3e^t	\frac{dy}{dt}-2y=3e^{t}
integral of sin^2(5x)cos^4(5x)	\int\:\sin^{2}(5x)\cos^{4}(5x)dx
integral from-3 to 3 of 9x^2	\int\:_{-3}^{3}9x^{2}dx
y^{''}-6y^'+9y=6x^2e^{3x}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=6x^{2}e^{3x}
integral of 1/(10x^4)	\int\:\frac{1}{10x^{4}}dx
derivative of (10/((x+5)^2))	\frac{d}{dx}(\frac{10}{(x+5)^{2}})
taylor x*sin(x)	taylor\:x\cdot\:\sin(x)
integral of (3(-5+ln(4x))^3)/x	\int\:\frac{3(-5+\ln(4x))^{3}}{x}dx
tangent of f(x)=x^2-9x+18,4,\at x=3	tangent\:f(x)=x^{2}-9x+18,4,\at\:x=3

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