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Popular Calculus Problems

(\partial)/(\partial x)((x+y)^{1/2})	\frac{\partial\:}{\partial\:x}((x+y)^{\frac{1}{2}})
(\partial)/(\partial x)(4x^3+y^2)	\frac{\partial\:}{\partial\:x}(4x^{3}+y^{2})
integral of x^2(5^3+7^2-6x-3)	\int\:x^{2}(5^{3}+7^{2}-6x-3)dx
area x=-2,x=1,y=e^x,y=3-e^x	area\:x=-2,x=1,y=e^{x},y=3-e^{x}
integral of (cot(x))[ln(sin(x))]	\int\:(\cot(x))[\ln(\sin(x))]dx
integral of x^2+x+6	\int\:x^{2}+x+6dx
integral of (3x^2+5x)/((x-1)(x+1)^2)	\int\:\frac{3x^{2}+5x}{(x-1)(x+1)^{2}}dx
(x+2y^2)dx+xydy=0	(x+2y^{2})dx+xydy=0
x^2y^{''}-3xy^'+4y=x,y(1)=0,y^'(1)=0	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+4y=x,y(1)=0,y^{\prime\:}(1)=0
(dy)/(dx)= x/(sqrt(x^2+64))	\frac{dy}{dx}=\frac{x}{\sqrt{x^{2}+64}}
sum from n=1 to infinity of n!(2x-1)^n	\sum\:_{n=1}^{\infty\:}n!(2x-1)^{n}
(dx)/(dt)=-8	\frac{dx}{dt}=-8
integral of (x^4+5x^3-3)/x	\int\:\frac{x^{4}+5x^{3}-3}{x}dx
integral of (6xy+4x)	\int\:(6xy+4x)dy
slope of (-5,-8),(9,-8)	slope\:(-5,-8),(9,-8)
limit as x approaches-9 of 5x-4	\lim\:_{x\to\:-9}(5x-4)
inverse oflaplace-(75)/(s^2+6s+25)	inverselaplace\:-\frac{75}{s^{2}+6s+25}
(dy)/(dx)=((x^2+xy+y^2))/(x^2)	\frac{dy}{dx}=\frac{(x^{2}+xy+y^{2})}{x^{2}}
limit as h approaches 0 of (h^2)/(3\|h\|)	\lim\:_{h\to\:0}(\frac{h^{2}}{3\left\|h\right\|})
integral of 1/(sin(x)-1)	\int\:\frac{1}{\sin(x)-1}dx
derivative of ln(4x+9)	\frac{d}{dx}(\ln(4x+9))
limit as x approaches-6 of (x^2-5)/(6-x)	\lim\:_{x\to\:-6}(\frac{x^{2}-5}{6-x})
ty^'+y=t^2	ty^{\prime\:}+y=t^{2}
(dy)/(dx)= 1/(2x+y+1)	\frac{dy}{dx}=\frac{1}{2x+y+1}
integral of 1/(2y)	\int\:\frac{1}{2y}dy
integral from 0 to 8 of \|sqrt(5x+6)-x\|	\int\:_{0}^{8}\left\|\sqrt{5x+6}-x\right\|dx
derivative of sqrt(3x-7)	\frac{d}{dx}(\sqrt{3x-7})
limit as x approaches 0 of \|7x\|	\lim\:_{x\to\:0}(\left\|7x\right\|)
tangent of y=x^2+8	tangent\:y=x^{2}+8
(arctan(4x))^'	(\arctan(4x))^{\prime\:}
derivative of 7x^2(x-4)^3	derivative\:7x^{2}(x-4)^{3}
integral of (5x^2)/(sqrt(4x-x^2))	\int\:\frac{5x^{2}}{\sqrt{4x-x^{2}}}dx
integral of 4/u	\int\:\frac{4}{u}du
sum from n=2 to infinity of e^{5-2n}	\sum\:_{n=2}^{\infty\:}e^{5-2n}
x^2y^'+y^2-xy=0	x^{2}y^{\prime\:}+y^{2}-xy=0
integral of (sqrt(x-3))/(x+4)	\int\:\frac{\sqrt{x-3}}{x+4}dx
integral of-16x	\int\:-16xdx
integral of (x+1)^{10}(x+2)	\int\:(x+1)^{10}(x+2)dx
derivative of 1/(x-6)	derivative\:\frac{1}{x-6}
area x, 1/x , 1/2	area\:x,\frac{1}{x},\frac{1}{2}
derivative of y=ln(sec(x))	derivative\:y=\ln(\sec(x))
limit as x approaches 0 of (1/x)^{x^2}	\lim\:_{x\to\:0}((\frac{1}{x})^{x^{2}})
(\partial)/(\partial x)(((1+y))/(1+x))	\frac{\partial\:}{\partial\:x}(\frac{(1+y)}{1+x})
limit as x approaches-1 of x^4-x^3+2x	\lim\:_{x\to\:-1}(x^{4}-x^{3}+2x)
derivative of e^{-2x}(acos(x+bsin(x)))	\frac{d}{dx}(e^{-2x}(a\cos(x)+b\sin(x)))
limit as x approaches 0+of 6/(sin(x))	\lim\:_{x\to\:0+}(\frac{6}{\sin(x)})
integral of 1/(v^2+8v-9)	\int\:\frac{1}{v^{2}+8v-9}dv
integral of-2/(x+1)	\int\:-\frac{2}{x+1}dx
integral of sqrt(x)(3x-2)	\int\:\sqrt{x}(3x-2)dx
(dy)/(dx)+xy=y	\frac{dy}{dx}+xy=y
integral from-1 to 9 of 9-x^2+8x	\int\:_{-1}^{9}9-x^{2}+8xdx
y^'=(5xsec(y/x)+y)/x	y^{\prime\:}=\frac{5x\sec(\frac{y}{x})+y}{x}
laplacetransform 3cos(t+pi/3)	laplacetransform\:3\cos(t+\frac{π}{3})
simplify (sqrt(x)+1/(\sqrt[3]{x)})^2	simplify\:(\sqrt{x}+\frac{1}{\sqrt[3]{x}})^{2}
derivative of cot(7x)	\frac{d}{dx}(\cot(7x))
integral of 1/(x^2)-1/(x^3)	\int\:\frac{1}{x^{2}}-\frac{1}{x^{3}}dx
limit as x approaches 0 of 1/(2x-1)	\lim\:_{x\to\:0}(\frac{1}{2x-1})
d/(du)(x^2+x{y}(x,u)(x,u)^3)	\frac{d}{du}(x^{2}+x{y}(x,u)(x,u)^{3})
limit as x approaches-1-of x-1	\lim\:_{x\to\:-1-}(x-1)
integral of sqrt(t)ln(t)	\int\:\sqrt{t}\ln(t)dt
integral of x^{5/4}	\int\:x^{\frac{5}{4}}dx
t^2(d^2y)/(dt^2)+2t(dy)/(dt)-6y=0	t^{2}\frac{d^{2}y}{dt^{2}}+2t\frac{dy}{dt}-6y=0
derivative of (4x^2+4x+4/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+4x+4}{\sqrt{x}})
inverse oflaplace (4s+3)/(s^2+109s+990)	inverselaplace\:\frac{4s+3}{s^{2}+109s+990}
tangent of (x+2)^2+(y-3)^2=37,(-8,4)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-8,4)
integral of cos^2(u)sin^2(u)	\int\:\cos^{2}(u)\sin^{2}(u)du
integral of (x+1)cos(2x^2+4x)	\int\:(x+1)\cos(2x^{2}+4x)dx
derivative of 6x^5e^{6x}	\frac{d}{dx}(6x^{5}e^{6x})
derivative of (1-2x/(6+x))	\frac{d}{dx}(\frac{1-2x}{6+x})
integral of (x^3)/(2x^2-x-1)	\int\:\frac{x^{3}}{2x^{2}-x-1}dx
tangent of f(x)=4x-3sqrt(x)	tangent\:f(x)=4x-3\sqrt{x}
derivative of ax^n	\frac{d}{dx}(ax^{n})
derivative of 1/(sqrt(x^4+1))	\frac{d}{dx}(\frac{1}{\sqrt{x^{4}+1}})
integral of (8^x-sec^2(x))	\int\:(8^{x}-\sec^{2}(x))dx
x^2y^{''}-2xy^'-40y=x^4	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}-40y=x^{4}
integral of 1/(t^2sqrt(225-t^2))	\int\:\frac{1}{t^{2}\sqrt{225-t^{2}}}dt
limit as x approaches 1+of-6	\lim\:_{x\to\:1+}(-6)
derivative of (7x+8)^2	derivative\:(7x+8)^{2}
(\partial}{\partial x}(\frac{-y+sqrt(y^2+4x^2))/2)	\frac{\partial\:}{\partial\:x}(\frac{-y+\sqrt{y^{2}+4x^{2}}}{2})
derivative of 6-x	\frac{d}{dx}(6-x)
sum from k=1 to infinity of (k!)/(2^k)	\sum\:_{k=1}^{\infty\:}\frac{k!}{2^{k}}
integral from-1 to 1 of x^3	\int\:_{-1}^{1}x^{3}dx
derivative of cos(5sqrt(12-4x^3))	\frac{d}{dx}(\cos(5\sqrt{12-4x^{3}}))
integral from 2 to 5 of (x-3)^2	\int\:_{2}^{5}(x-3)^{2}dx
(\partial)/(\partial z)(-5e^xcos(yz))	\frac{\partial\:}{\partial\:z}(-5e^{x}\cos(yz))
tangent of y=3x+8cos(x),(0,8)	tangent\:y=3x+8\cos(x),(0,8)
limit as x approaches 3+of (x-1)/(3-x)	\lim\:_{x\to\:3+}(\frac{x-1}{3-x})
integral of 15tan^2(x)sec^3(x)	\int\:15\tan^{2}(x)\sec^{3}(x)dx
derivative of 2xe^{4x}	derivative\:2xe^{4x}
d/(dθ)(4sin(2θ))	\frac{d}{dθ}(4\sin(2θ))
integral of 2/(x^3sqrt(x^2-3))	\int\:\frac{2}{x^{3}\sqrt{x^{2}-3}}dx
derivative of sqrt(2)x+sqrt(3x)	derivative\:\sqrt{2}x+\sqrt{3x}
y^{''}-3y^'+2y=e^{3x}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{3x}
inverse oflaplace s/(s^2+2s+5)	inverselaplace\:\frac{s}{s^{2}+2s+5}
limit as x approaches infinity of 1/x+5	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+5)
integral from 0 to 1 of e^{4x}	\int\:_{0}^{1}e^{4x}dx
integral of sin(9x)cos(7x)	\int\:\sin(9x)\cos(7x)dx
integral of xcos^2(7x)	\int\:x\cos^{2}(7x)dx
(sin(5x))^'	(\sin(5x))^{\prime\:}
slope of f(x)=sqrt(x)+1/(sqrt(x))	slope\:f(x)=\sqrt{x}+\frac{1}{\sqrt{x}}

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