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Popular Calculus Problems

(\partial)/(\partial x)(sqrt(t^4+x^3))	\frac{\partial\:}{\partial\:x}(\sqrt{t^{4}+x^{3}})
integral of 4cos(x)	\int\:4\cos(x)dx
integral of 1/(sqrt(22-x^2))	\int\:\frac{1}{\sqrt{22-x^{2}}}dx
sum from n=0 to infinity of 6(1/7)^n	\sum\:_{n=0}^{\infty\:}6(\frac{1}{7})^{n}
limit as x approaches 2-of (x+2)/(x-4)	\lim\:_{x\to\:2-}(\frac{x+2}{x-4})
sum from n=-infinity to infinity of 7^2	\sum\:_{n=-\infty\:}^{\infty\:}7^{2}
limit as x approaches 2 of (3x)/(x-4)	\lim\:_{x\to\:2}(\frac{3x}{x-4})
y^{''}+2x=0	y^{\prime\:\prime\:}+2x=0
(\partial)/(\partial x)(2x^2y-x+3y^3)	\frac{\partial\:}{\partial\:x}(2x^{2}y-x+3y^{3})
derivative of (x-2(-x+2)(x^2+3x-3))	\frac{d}{dx}((x-2)(-x+2)(x^{2}+3x-3))
y^{''}-8y^'+15y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=0
limit as x approaches infinity of csc(9)	\lim\:_{x\to\:\infty\:}(\csc(9))
derivative of y=(4x-1)^2(x^4+1)^2	derivative\:y=(4x-1)^{2}(x^{4}+1)^{2}
(\partial)/(\partial x)((xz+yz)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{xz+yz}{xy})
derivative of f(x)=(sqrt(x))/(2+x)	derivative\:f(x)=\frac{\sqrt{x}}{2+x}
derivative of A/x	\frac{d}{dx}(\frac{A}{x})
limit as x approaches 1 of x^2+2x-5/2	\lim\:_{x\to\:1}(x^{2}+2x-\frac{5}{2})
(x^2+1)(dy)/(dx)+4x(y-1)=0,y(0)=8	(x^{2}+1)\frac{dy}{dx}+4x(y-1)=0,y(0)=8
integral from-1 to 1 of e^y-(y^2-7)	\int\:_{-1}^{1}e^{y}-(y^{2}-7)dy
derivative of log_{9}(-(x-4(5x-2)))	\frac{d}{dx}(\log_{9}(-(x-4)(5x-2)))
(\partial)/(\partial y)(sin(x)y)	\frac{\partial\:}{\partial\:y}(\sin(x)y)
derivative of f(x)=(x^5+x^9)/x	derivative\:f(x)=\frac{x^{5}+x^{9}}{x}
derivative of y=8e^{-x}+e^{3x}	derivative\:y=8e^{-x}+e^{3x}
limit as x approaches 0 of 1-(cos(x))/x	\lim\:_{x\to\:0}(1-\frac{\cos(x)}{x})
derivative of (sqrt(5+x)-sqrt(5))/x	derivative\:\frac{\sqrt{5+x}-\sqrt{5}}{x}
dy-(y-8)^2dx=0	dy-(y-8)^{2}dx=0
(\partial)/(\partial x)(x^2y^3+(x-y)^2)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+(x-y)^{2})
xy^'+y=-3xy^2,y(1)=4	xy^{\prime\:}+y=-3xy^{2},y(1)=4
integral of 17sin^2(2x)	\int\:17\sin^{2}(2x)dx
integral of (ln(x))/(x^{10)}	\int\:\frac{\ln(x)}{x^{10}}dx
sum from n=3 to infinity of cos(npi)	\sum\:_{n=3}^{\infty\:}\cos(nπ)
lcm 1,0(1.03^x)	lcm\:1,0(1.03^{x})
integral from 1 to 3 of (6x^2-4x+5)	\int\:_{1}^{3}(6x^{2}-4x+5)dx
integral of 1/(3+tan^2(x))	\int\:\frac{1}{3+\tan^{2}(x)}dx
integral from 0 to infinity of e^{3x}	\int\:_{0}^{\infty\:}e^{3x}dx
limit as x approaches infinity of (x-1)^{1/(ln(x))}	\lim\:_{x\to\:\infty\:}((x-1)^{\frac{1}{\ln(x)}})
derivative of e^{{p}(t,xt}*cos(nt))	\frac{d}{dx}(e^{{p}(t,x)t}\cdot\:\cos(nt))
(\partial)/(\partial x)(sqrt(6-x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{6-x^{2}+2y^{2}})
derivative of Ax^2	\frac{d}{dx}(Ax^{2})
integral of (x+3)/(x^2-2x-3)	\int\:\frac{x+3}{x^{2}-2x-3}dx
integral of f(x+b)	\int\:f(x+b)dx
derivative of sqrt(x+2)	derivative\:\sqrt{x+2}
tangent of 2x^3-4x^2,\at x=1	tangent\:2x^{3}-4x^{2},\at\:x=1
integral of 14ln(\sqrt[3]{x})	\int\:14\ln(\sqrt[3]{x})dx
derivative of y= 7/x+6sec(x)	derivative\:y=\frac{7}{x}+6\sec(x)
(\partial)/(\partial y)((3x)/((x+y)^4))	\frac{\partial\:}{\partial\:y}(\frac{3x}{(x+y)^{4}})
integral of 3x^2-3	\int\:3x^{2}-3dx
f^'(x)=3e^x+7sec^2(x)	f^{\prime\:}(x)=3e^{x}+7\sec^{2}(x)
2y^{''}+y^'-y=x+5	2y^{\prime\:\prime\:}+y^{\prime\:}-y=x+5
(x+y)^2dx+(2xy+x^2-8)dy=0,y(1)=1	(x+y)^{2}dx+(2xy+x^{2}-8)dy=0,y(1)=1
derivative of ln((x-2/(x+2)))	\frac{d}{dx}(\ln(\frac{x-2}{x+2}))
3y^{''}-10y^'+3y=0,y(0)=-5,y^'(0)=-1	3y^{\prime\:\prime\:}-10y^{\prime\:}+3y=0,y(0)=-5,y^{\prime\:}(0)=-1
integral from 0 to pi of sin^2(x)cos(x)	\int\:_{0}^{π}\sin^{2}(x)\cos(x)dx
tangent of f(x)=(6x-5)^{1/2},\at x=1	tangent\:f(x)=(6x-5)^{\frac{1}{2}},\at\:x=1
(dy)/(dx)=8x^{-9}	\frac{dy}{dx}=8x^{-9}
derivative of 2/3 x^3-3/(4x^2)	\frac{d}{dx}(\frac{2}{3}x^{3}-\frac{3}{4x^{2}})
derivative of y=sin(tan(5x))	derivative\:y=\sin(\tan(5x))
integral of (sqrt(t^9+4t))(9t^8+4)	\int\:(\sqrt{t^{9}+4t})(9t^{8}+4)dt
integral of (4x-2/x)	\int\:(4x-\frac{2}{x})dx
integral of 2/((x-3)^2)	\int\:\frac{2}{(x-3)^{2}}dx
f(x)=x^3e^{-x^3}+sqrt(5)	f(x)=x^{3}e^{-x^{3}}+\sqrt{5}
integral of ((x-1)(x^2+4))/(x(x+1))	\int\:\frac{(x-1)(x^{2}+4)}{x(x+1)}dx
integral of (-5x^2+11x-10)/(x^3-x^2-6x)	\int\:\frac{-5x^{2}+11x-10}{x^{3}-x^{2}-6x}dx
derivative of (40x^5)/(e^x)	derivative\:\frac{40x^{5}}{e^{x}}
derivative of 2/(x-7)	\frac{d}{dx}(\frac{2}{x-7})
(4xy+3y^2-x)dx+(x^2+2xy)dy=0	(4xy+3y^{2}-x)dx+(x^{2}+2xy)dy=0
tangent of y=(x^2)/(x+4),(3, 9/7)	tangent\:y=\frac{x^{2}}{x+4},(3,\frac{9}{7})
integral from-7 to 7 of (49-x^2)^{1/2}	\int\:_{-7}^{7}(49-x^{2})^{\frac{1}{2}}dx
y^'+xy=6xy^2	y^{\prime\:}+xy=6xy^{2}
integral of x^2+2^x	\int\:x^{2}+2^{x}dx
(\partial)/(\partial y)((x-2y)/(x+2))	\frac{\partial\:}{\partial\:y}(\frac{x-2y}{x+2})
integral from 0 to 3 of pi(3x)^2	\int\:_{0}^{3}π(3x)^{2}dx
(6+x)(dy)/(dx)=9y	(6+x)\frac{dy}{dx}=9y
integral of (xln(14x))	\int\:(x\ln(14x))dx
limit as x approaches 2+of (3x^2)/(x-2)	\lim\:_{x\to\:2+}(\frac{3x^{2}}{x-2})
integral of 8sin^4(x)	\int\:8\sin^{4}(x)dx
integral of (sqrt(x))/(x^2)	\int\:\frac{\sqrt{x}}{x^{2}}dx
limit as x approaches 0 of x/(cot(5x))	\lim\:_{x\to\:0}(\frac{x}{\cot(5x)})
integral of 1/(1+v^2)	\int\:\frac{1}{1+v^{2}}dv
limit as x approaches 2 of-4	\lim\:_{x\to\:2}(-4)
integral of xe^{-x(1+y)}	\int\:xe^{-x(1+y)}dx
laplacetransform e^{2t}tsin(5t)	laplacetransform\:e^{2t}t\sin(5t)
sum from n=0 to infinity of (-1)^nx^{2n}	\sum\:_{n=0}^{\infty\:}(-1)^{n}x^{2n}
tangent of y=(3x+1)/(x^2+1),(1,2)	tangent\:y=\frac{3x+1}{x^{2}+1},(1,2)
area y=x^2-3x,y=5x	area\:y=x^{2}-3x,y=5x
y^'=5y+y^5,y(0)=1	y^{\prime\:}=5y+y^{5},y(0)=1
limit as x approaches 2-of x^2+3x	\lim\:_{x\to\:2-}(x^{2}+3x)
integral of sqrt(x)-1/2 x+2/(sqrt(x))	\int\:\sqrt{x}-\frac{1}{2}x+\frac{2}{\sqrt{x}}dx
integral of sec(1/2)xtan(1/2)x	\int\:\sec(\frac{1}{2})x\tan(\frac{1}{2})xdx
(\partial)/(\partial x)(2(y/x)^{1/2})	\frac{\partial\:}{\partial\:x}(2(\frac{y}{x})^{\frac{1}{2}})
derivative of f(x)=sqrt(3x+3)	derivative\:f(x)=\sqrt{3x+3}
(d^2)/(dx^2)(kx)	\frac{d^{2}}{dx^{2}}(kx)
sum from n=1 to infinity of (x^n)/(n*5n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{n\cdot\:5n}
derivative of (x^3-16x^{10})	\frac{d}{dx}((x^{3}-16x)^{10})
d/(dt)(sqrt(1+t))	\frac{d}{dt}(\sqrt{1+t})
(dy)/(dt)=2t+y+1	\frac{dy}{dt}=2t+y+1
integral from 0 to 2pi of 2x	\int\:_{0}^{2π}2xdx
derivative of y=x(x^3+7)^4	derivative\:y=x(x^{3}+7)^{4}
(\partial)/(\partial x)(1/(2x+1))	\frac{\partial\:}{\partial\:x}(\frac{1}{2x+1})
sum from n=0 to infinity of (-3/5)^n	\sum\:_{n=0}^{\infty\:}(-\frac{3}{5})^{n}

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