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Popular Calculus Problems

f(x)=xcos(x^2)	f(x)=x\cos(x^{2})
integral of 2/(2x^2+4x-6)	\int\:\frac{2}{2x^{2}+4x-6}dx
integral of e^{x^3}6x^2	\int\:e^{x^{3}}6x^{2}dx
integral of (2x+3)/(9-4x^2)	\int\:\frac{2x+3}{9-4x^{2}}dx
(\partial)/(\partial x)(5x^4y^6+3x^5y^8)	\frac{\partial\:}{\partial\:x}(5x^{4}y^{6}+3x^{5}y^{8})
limit as x approaches 0 of ((6^x-4^x))/x	\lim\:_{x\to\:0}(\frac{(6^{x}-4^{x})}{x})
derivative of (9x)/(9x-5)	derivative\:\frac{9x}{9x-5}
(y+4)*y^'=2xy+4y	(y+4)\cdot\:y^{\prime\:}=2xy+4y
sum from n=0 to infinity of (x/2)^n	\sum\:_{n=0}^{\infty\:}(\frac{x}{2})^{n}
(2x+ye^{y/x})dx-xe^{y/x}dy=0	(2x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
derivative of ln((cos(x)/x))	\frac{d}{dx}(\ln(\frac{\cos(x)}{x}))
derivative of (4x+5x^2^4)	\frac{d}{dx}((4x+5x^{2})^{4})
integral of (sqrt(16-x^2))/(x^2)	\int\:\frac{\sqrt{16-x^{2}}}{x^{2}}dx
integral of 1/(sqrt(8x-x^2))	\int\:\frac{1}{\sqrt{8x-x^{2}}}dx
derivative of 5\sqrt[3]{x}	derivative\:5\sqrt[3]{x}
(\partial)/(\partial y)(xln(yz))	\frac{\partial\:}{\partial\:y}(x\ln(yz))
integral of x^4+10x^2+25	\int\:x^{4}+10x^{2}+25dx
y^'+1/2 y=17sin(2t)	y^{\prime\:}+\frac{1}{2}y=17\sin(2t)
derivative of y=4^{9^{x^2}}	derivative\:y=4^{9^{x^{2}}}
integral of (x^2+8x-1)/(x^3-x)	\int\:\frac{x^{2}+8x-1}{x^{3}-x}dx
limit as x approaches-1 of 2x^2-2/(x-1)	\lim\:_{x\to\:-1}(2x^{2}-\frac{2}{x-1})
(\partial)/(\partial x)(x^9y^4-x^6+y^8)	\frac{\partial\:}{\partial\:x}(x^{9}y^{4}-x^{6}+y^{8})
slope ofintercept (-5,1),(-4,-7)	slopeintercept\:(-5,1),(-4,-7)
tangent of x/(e^x)	tangent\:\frac{x}{e^{x}}
sum from n=0 to infinity of (-1)^{n+1}	\sum\:_{n=0}^{\infty\:}(-1)^{n+1}
simplify-7	simplify\:-7
derivative of y=te^{-t}	derivative\:y=te^{-t}
xy^2(dy)/(dx)=y^3-x^3,y(1)=3	xy^{2}\frac{dy}{dx}=y^{3}-x^{3},y(1)=3
integral of x/(2x-1)	\int\:\frac{x}{2x-1}dx
y^'= x/(10y)	y^{\prime\:}=\frac{x}{10y}
integral of sec(x)tan^5(x)	\int\:\sec(x)\tan^{5}(x)dx
(\partial)/(\partial x)(x+xy+y)	\frac{\partial\:}{\partial\:x}(x+xy+y)
area (2x)/(x^2+1), x/(13),[-5,5]	area\:\frac{2x}{x^{2}+1},\frac{x}{13},[-5,5]
area 3sin(x),4cos(x)	area\:3\sin(x),4\cos(x)
implicit x+5xy-2x^3=2	implicit\:x+5xy-2x^{3}=2
y^{''}=xsin(x)+xcos(x)	y^{\prime\:\prime\:}=x\sin(x)+x\cos(x)
integral of x(x^2+3)	\int\:x(x^{2}+3)dx
sum from n=0 to infinity of (n+1)0.5^n	\sum\:_{n=0}^{\infty\:}(n+1)0.5^{n}
derivative of sin(x+sin(4x))	derivative\:\sin(x+\sin(4x))
y^'=(1-2x)y^2	y^{\prime\:}=(1-2x)y^{2}
sum from n=1 to infinity of (15^n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{15^{n}}{n!}
derivative of 4xe^{2x}	\frac{d}{dx}(4xe^{2x})
derivative of x,y	\frac{d}{dx}(x,y)
limit as x approaches 0 of ((x^2+1))/x	\lim\:_{x\to\:0}(\frac{(x^{2}+1)}{x})
integral from 0 to 1 of sqrt(x^4+2x^2+1)	\int\:_{0}^{1}\sqrt{x^{4}+2x^{2}+1}dx
integral of x(3+2/x)^2	\int\:x(3+\frac{2}{x})^{2}dx
integral of p(p+9)^7	\int\:p(p+9)^{7}dp
integral of 1-(cos(x))^2	\int\:1-(\cos(x))^{2}dx
(\partial)/(\partial x)(-2x^3+6y^2+8xy)	\frac{\partial\:}{\partial\:x}(-2x^{3}+6y^{2}+8xy)
tangent of f(x)=x^4+2e^x,(0,2)	tangent\:f(x)=x^{4}+2e^{x},(0,2)
derivative of 3x^2+7	\frac{d}{dx}(3x^{2}+7)
derivative of (x-1/(x+4))	\frac{d}{dx}(\frac{x-1}{x+4})
integral of cos(5x)cos(2x)	\int\:\cos(5x)\cos(2x)dx
y^'+e^xy=sin(x)	y^{\prime\:}+e^{x}y=\sin(x)
integral from 1 to 3 of (x^2-1/(4x^2))	\int\:_{1}^{3}(x^{2}-\frac{1}{4x^{2}})dx
(dy)/(dx)=(2x+y)/(2x+y+3)	\frac{dy}{dx}=\frac{2x+y}{2x+y+3}
expand ((x^{(3)}-1)(x+1)^{(3)})/(x+2)	expand\:\frac{(x^{(3)}-1)(x+1)^{(3)}}{x+2}
derivative of 7z+6z^{1/2}-8	derivative\:7z+6z^{\frac{1}{2}}-8
derivative of (3cos(x)(ln(1+x)))	\frac{d}{dx}((3\cos(x))(\ln(1+x)))
derivative of ln\|tan(x+sec(x)\|+C)	\frac{d}{dx}(\ln\left\|\tan(x)+\sec(x)\right\|+C)
derivative of (9x^2+6)^6	derivative\:(9x^{2}+6)^{6}
integral of (7sec^2(2x))/(3-5tan(2x))	\int\:\frac{7\sec^{2}(2x)}{3-5\tan(2x)}dx
derivative of 2/(1-7x)	\frac{d}{dx}(\frac{2}{1-7x})
sum from n=0 to infinity of 1/(n+5)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+5}
integral of (x^2)/((64-x^2)^{3/2)}	\int\:\frac{x^{2}}{(64-x^{2})^{\frac{3}{2}}}dx
(e^{-t}cos(t))^'	(e^{-t}\cos(t))^{\prime\:}
integral of 6^x	\int\:6^{x}dx
integral of arcsinh(x)	\int\:\arcsinh(x)dx
(\partial)/(\partial x)(-yx)	\frac{\partial\:}{\partial\:x}(-yx)
integral of 2e^{x/2}	\int\:2e^{\frac{x}{2}}dx
integral of 1/(x(\sqrt[6]{x))}	\int\:\frac{1}{x(\sqrt[6]{x})}dx
limit as x approaches+0+of x^{12}ln(x)	\lim\:_{x\to\:+0+}(x^{12}\ln(x))
integral of x^7e^{x^8}	\int\:x^{7}e^{x^{8}}dx
integral from 1 to 3 of (x^2+2)/(4x-x^2)	\int\:_{1}^{3}\frac{x^{2}+2}{4x-x^{2}}dx
integral of (3x^2)/(x^3+1)	\int\:\frac{3x^{2}}{x^{3}+1}dx
y(x-b)+y^'bx=0	y(x-b)+y^{\prime\:}bx=0
y^'=(-y^3+14x-8)/(3xy^2)	y^{\prime\:}=\frac{-y^{3}+14x-8}{3xy^{2}}
derivative of 2/(2x^4-5)	\frac{d}{dx}(\frac{2}{2x^{4}-5})
derivative of ((x+1^2+(x-1)^2)/(x^2))	\frac{d}{dx}(\frac{(x+1)^{2}+(x-1)^{2}}{x^{2}})
integral of (2x+3)/(x^2+2x+5)	\int\:\frac{2x+3}{x^{2}+2x+5}dx
(\partial)/(\partial x)(e^{-y/(x^2+y^2+1)})	\frac{\partial\:}{\partial\:x}(e^{-\frac{y}{x^{2}+y^{2}+1}})
slope of (-3.7)(0.3)	slope\:(-3.7)(0.3)
derivative of 3*4^{x^2+2}	\frac{d}{dx}(3\cdot\:4^{x^{2}+2})
integral of 1/(sqrt((x+1)^2+25))	\int\:\frac{1}{\sqrt{(x+1)^{2}+25}}dx
(\partial)/(\partial x)(90-4x^2-y^2)	\frac{\partial\:}{\partial\:x}(90-4x^{2}-y^{2})
integral from-1 to 3 of 3x^2+6x	\int\:_{-1}^{3}3x^{2}+6xdx
taylor 6/(1+36x^2)	taylor\:\frac{6}{1+36x^{2}}
integral from 1 to 3 of xe^{x^2}	\int\:_{1}^{3}xe^{x^{2}}dx
derivative of ln(sqrt((3x^4+2)/(4x)))	derivative\:\ln(\sqrt{\frac{3x^{4}+2}{4x}})
(\partial)/(\partial x)(y^3e^{2x}+5sin(xy))	\frac{\partial\:}{\partial\:x}(y^{3}e^{2x}+5\sin(xy))
derivative of sqrt(x^2+3x)-x	\frac{d}{dx}(\sqrt{x^{2}+3x}-x)
y^{''}+6y=0,y^'(1)=5	y^{\prime\:\prime\:}+6y=0,y^{\prime\:}(1)=5
(dy)/(dx)=((x^2+1))/(y^2+1),y(0)=1	\frac{dy}{dx}=\frac{(x^{2}+1)}{y^{2}+1},y(0)=1
derivative of arccos(1-2x^2)	\frac{d}{dx}(\arccos(1-2x^{2}))
limit as x approaches 3 of (\sqrt[3]{x^2-1}-2)/(x-3)	\lim\:_{x\to\:3}(\frac{\sqrt[3]{x^{2}-1}-2}{x-3})
area y=6-6x,y=0,x=0	area\:y=6-6x,y=0,x=0
(\partial)/(\partial x)(-x^2+2xy-y^2)	\frac{\partial\:}{\partial\:x}(-x^{2}+2xy-y^{2})
limit as x approaches-3 of 2x+\|x-3\|	\lim\:_{x\to\:-3}(2x+\left\|x-3\right\|)
integral of csc^4(3x)	\int\:\csc^{4}(3x)dx
integral of x/(1-x^2)	\int\:\frac{x}{1-x^{2}}dx

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