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Popular Calculus Problems

sum from n=0 to infinity of 5	\sum\:_{n=0}^{\infty\:}5
integral of 1/((x-2)(x-4))	\int\:\frac{1}{(x-2)(x-4)}dx
(\partial)/(\partial y)(x^3+y^3-6xy)	\frac{\partial\:}{\partial\:y}(x^{3}+y^{3}-6xy)
(\partial)/(\partial x)((x^2-x)/((L+2x)^3))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-x}{(L+2x)^{3}})
limit as x approaches+2-of sqrt(x+c)	\lim\:_{x\to\:+2-}(\sqrt{x+c})
derivative of 2/(9+x^2)	\frac{d}{dx}(\frac{2}{9+x^{2}})
derivative of e^2(2x+4)	\frac{d}{dx}(e^{2}(2x+4))
integral of 4sin^3(x)cos^5(x)	\int\:4\sin^{3}(x)\cos^{5}(x)dx
derivative of 40cos(pix)	\frac{d}{dx}(40\cos(π)x)
integral from 0 to 3 of xe^{4x}	\int\:_{0}^{3}xe^{4x}dx
derivative of 3sin(t)	derivative\:3\sin(t)
limit as x approaches 0 of (3x)/x	\lim\:_{x\to\:0}(\frac{3x}{x})
tangent of f(x)= 2/x ,(-6,-1/3)	tangent\:f(x)=\frac{2}{x},(-6,-\frac{1}{3})
(dy)/(dx)=4y^3	\frac{dy}{dx}=4y^{3}
(2xy+y)dx+(x^2-x)dy=0	(2xy+y)dx+(x^{2}-x)dy=0
(dy)/(dx)-y/x =x^2	\frac{dy}{dx}-\frac{y}{x}=x^{2}
limit as x approaches 0+of 12cos(12x)	\lim\:_{x\to\:0+}(12\cos(12x))
xy^'+2y=sin(x),y(pi)= 1/pi	xy^{\prime\:}+2y=\sin(x),y(π)=\frac{1}{π}
integral of 1/(sqrt(r^2-x^2))	\int\:\frac{1}{\sqrt{r^{2}-x^{2}}}dx
implicit (dy)/(dx),xy=6	implicit\:\frac{dy}{dx},xy=6
(\partial)/(\partial y)(x+2y^{1/2})	\frac{\partial\:}{\partial\:y}(x+2y^{\frac{1}{2}})
derivative of y= 7/(sqrt(x-1))	derivative\:y=\frac{7}{\sqrt{x-1}}
derivative of 4cos(5ln(x))	derivative\:4\cos(5\ln(x))
factor (cos(t)+tsin(t))+(sin(t)-tcos(t))	factor\:(\cos(t)+t\sin(t))+(\sin(t)-t\cos(t))
integral of 9x^4cos(x^5+6)	\int\:9x^{4}\cos(x^{5}+6)dx
(\partial)/(\partial x)(asin(x)cos(y))	\frac{\partial\:}{\partial\:x}(a\sin(x)\cos(y))
y^{''}+841y=sec(29x)	y^{\prime\:\prime\:}+841y=\sec(29x)
integral of 1/(2*x^2-x-3)	\int\:\frac{1}{2\cdot\:x^{2}-x-3}dx
(\partial)/(\partial s)(e^{st})	\frac{\partial\:}{\partial\:s}(e^{st})
integral of (2sin(x)-3cos(x)+1/2)	\int\:(2\sin(x)-3\cos(x)+\frac{1}{2})dx
integral of csc^2(t)	\int\:\csc^{2}(t)dt
inverse oflaplace 2/((s+3)^2-9)	inverselaplace\:\frac{2}{(s+3)^{2}-9}
integral of csc^2(5y)	\int\:\csc^{2}(5y)dy
area y= 1/x ,y= 1/(x^2),x=3	area\:y=\frac{1}{x},y=\frac{1}{x^{2}},x=3
derivative of sqrt(xsin(x))	\frac{d}{dx}(\sqrt{x\sin(x)})
integral of (xe^x)/((x+1)^2)	\int\:\frac{xe^{x}}{(x+1)^{2}}dx
derivative of (5x^2-8xe^x)	\frac{d}{dx}((5x^{2}-8x)e^{x})
x^{''}-0x^'+x=0	x^{\prime\:\prime\:}-0x^{\prime\:}+x=0
integral of 6	\int\:6dx
(\partial)/(\partial y)((-y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{-y}{x^{2}+y^{2}})
integral from-infinity to 0 of e^{-x}	\int\:_{-\infty\:}^{0}e^{-x}dx
limit as x approaches 1 of x^2+3x-1	\lim\:_{x\to\:1}(x^{2}+3x-1)
limit as t approaches pi of tan((5t)/4)	\lim\:_{t\to\:π}(\tan(\frac{5t}{4}))
y^{''}+6y^'+13y=0,y(0)=0,y^'(0)=2	y^{\prime\:\prime\:}+6y^{\prime\:}+13y=0,y(0)=0,y^{\prime\:}(0)=2
(\partial)/(\partial x)(2ln(xz))	\frac{\partial\:}{\partial\:x}(2\ln(xz))
integral of ln(x)cos(x)	\int\:\ln(x)\cos(x)dx
(\partial)/(\partial x)((x^2-2y)(y^2-x))	\frac{\partial\:}{\partial\:x}((x^{2}-2y)(y^{2}-x))
derivative of (x+pi/x cos(x))	\frac{d}{dx}(\frac{x+π}{x}\cos(x))
integral of 2^{7-x}	\int\:2^{7-x}dx
integral of (e^{-x})/(cos^2(e^{-x))}	\int\:\frac{e^{-x}}{\cos^{2}(e^{-x})}dx
derivative of ln(sqrt(x^2-7))	derivative\:\ln(\sqrt{x^{2}-7})
integral of (x-1)/(sqrt(1-x^2))	\int\:\frac{x-1}{\sqrt{1-x^{2}}}dx
derivative of f(x)=x^2+8x+7	\frac{d}{dx}f(x)=x^{2}+8x+7
limit as x approaches 0 of (7x^5+5x^2+12x)/(3x^5+4x)	\lim\:_{x\to\:0}(\frac{7x^{5}+5x^{2}+12x}{3x^{5}+4x})
tangent of x^2-3xy=10	tangent\:x^{2}-3xy=10
y^'=(sec(y))/((x-3)^2)	y^{\prime\:}=\frac{\sec(y)}{(x-3)^{2}}
sum from n=0 to infinity of 2/1	\sum\:_{n=0}^{\infty\:}\frac{2}{1}
(\partial)/(\partial x)(sqrt(4x+y))	\frac{\partial\:}{\partial\:x}(\sqrt{4x+y})
derivative of (2/x-1/(x^2)^{1/2})	\frac{d}{dx}((\frac{2}{x}-\frac{1}{x^{2}})^{\frac{1}{2}})
integral of 2tan^4(x)sec^6(x)	\int\:2\tan^{4}(x)\sec^{6}(x)dx
(dy)/(dx)=(1-y)y-6	\frac{dy}{dx}=(1-y)y-6
inverse oflaplace 1/2-1/2*(1/(s+1))	inverselaplace\:\frac{1}{2}-\frac{1}{2}\cdot\:(\frac{1}{s+1})
integral of e^{ln(2x)}	\int\:e^{\ln(2x)}dx
limit as x approaches 0 of (5xcot(3x))/(2sec(x))	\lim\:_{x\to\:0}(\frac{5x\cot(3x)}{2\sec(x)})
derivative of f(t)=2tsin(pit)	derivative\:f(t)=2t\sin(πt)
integral of (4x^2+21x+54)/(x^2+6x+13)	\int\:\frac{4x^{2}+21x+54}{x^{2}+6x+13}dx
limit as x approaches 8 of 6x^2-9x+1	\lim\:_{x\to\:8}(6x^{2}-9x+1)
taylor (3/2)^x	taylor\:(\frac{3}{2})^{x}
y^{''}-4y^'+2y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}-4y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=1
(\partial)/(\partial y)(4e^xln(y))	\frac{\partial\:}{\partial\:y}(4e^{x}\ln(y))
derivative of sqrt(x)-1/(sqrt(x))	\frac{d}{dx}(\sqrt{x}-\frac{1}{\sqrt{x}})
(dy)/(dx)=e^{4x-y}	\frac{dy}{dx}=e^{4x-y}
derivative of-x^4	\frac{d}{dx}(-x^{4})
limit as h approaches 0 of ((-4+h)+4)/h	\lim\:_{h\to\:0}(\frac{(-4+h)+4}{h})
integral of (8x^2+5x+8)/((x^2+1)^2)	\int\:\frac{8x^{2}+5x+8}{(x^{2}+1)^{2}}dx
integral of 2sin(x)	\int\:2\sin(x)dx
integral of (e^{5x})/(1+e^{5x)}	\int\:\frac{e^{5x}}{1+e^{5x}}dx
integral of (x^2y^2)	\int\:(x^{2}y^{2})dx
derivative of x^2-5x+1/(x^{3/2)}	derivative\:x^{2}-5x+\frac{1}{x^{\frac{3}{2}}}
limit as x approaches 3 of (x-3)/(1+x)	\lim\:_{x\to\:3}(\frac{x-3}{1+x})
derivative of ((x^2+1)/((x^2-1)))	\frac{d}{dx}(\frac{(x^{2}+1)}{(x^{2}-1)})
tangent of 2/3 x^3+4x^2+6x-5	tangent\:\frac{2}{3}x^{3}+4x^{2}+6x-5
integral of (196)/(w^2sqrt(49-w^2))	\int\:\frac{196}{w^{2}\sqrt{49-w^{2}}}dw
integral of 1/(2sqrt(x)+3)	\int\:\frac{1}{2\sqrt{x}+3}dx
(\partial)/(\partial y)(2x(5+y)^{-1})	\frac{\partial\:}{\partial\:y}(2x(5+y)^{-1})
parity (sec(9x^2))/(tan(2x)*cos(x))	parity\:\frac{\sec(9x^{2})}{\tan(2x)\cdot\:\cos(x)}
y^'=3	y^{\prime\:}=3
derivative of 1+6x^{3/2}	derivative\:1+6x^{\frac{3}{2}}
derivative of (6e^x/(5e^x+7))	\frac{d}{dx}(\frac{6e^{x}}{5e^{x}+7})
derivative of a^x+x^a	\frac{d}{dx}(a^{x}+x^{a})
integral from 1 to 4 of (2x+1)/(2x)	\int\:_{1}^{4}\frac{2x+1}{2x}dx
derivative of sqrt(x)+4	\frac{d}{dx}(\sqrt{x}+4)
(\partial)/(\partial x)(xarctan(x/y))	\frac{\partial\:}{\partial\:x}(x\arctan(\frac{x}{y}))
limit as x approaches infinity of x+x^3	\lim\:_{x\to\:\infty\:}(x+x^{3})
integral of e^{-s^2}	\int\:e^{-s^{2}}ds
limit as h approaches 0 of (2.7^h-1)/h	\lim\:_{h\to\:0}(\frac{2.7^{h}-1}{h})
(\partial)/(\partial x)(y/t)	\frac{\partial\:}{\partial\:x}(\frac{y}{t})
integral of 1/(sqrt(-x^2+12x-32))	\int\:\frac{1}{\sqrt{-x^{2}+12x-32}}dx
(\partial)/(\partial x)(2y+xe^{xy})	\frac{\partial\:}{\partial\:x}(2y+xe^{xy})
sum from n=1 to infinity of 1/(2^{2n-1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{2n-1}}

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