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Popular Calculus Problems

(dy)/(dx)+(2x)/(1+x^2)y=-2xy^2	\frac{dy}{dx}+\frac{2x}{1+x^{2}}y=-2xy^{2}
integral from 1 to x of 2(x-1)	\int\:_{1}^{x}2(x-1)dx
derivative of f(x)=arctan(x^{10})	derivative\:f(x)=\arctan(x^{10})
laplacetransform 3t^4+7t^2-5	laplacetransform\:3t^{4}+7t^{2}-5
integral of 6+3cos(x)	\int\:6+3\cos(x)dx
integral of 5/(x(x^4+7))	\int\:\frac{5}{x(x^{4}+7)}dx
derivative of (2+e^x/(2-e^{-x)})	\frac{d}{dx}(\frac{2+e^{x}}{2-e^{-x}})
integral of (x-2)/(x+1)	\int\:\frac{x-2}{x+1}dx
limit as h approaches 0 of (f(h)(8+h)-f(8))/h	\lim\:_{h\to\:0}(\frac{f(h)(8+h)-f(8)}{h})
slope of (-5,-10),(-1,5)	slope\:(-5,-10),(-1,5)
inverse oflaplace ((2-5s))/(s^2+9)	inverselaplace\:\frac{(2-5s)}{s^{2}+9}
derivative of 1/({g(x)})	\frac{d}{dx}(\frac{1}{{g}(x)})
integral of 8^{3x-1}	\int\:8^{3x-1}dx
derivative of 24x-176	derivative\:24x-176
integral from 3 to 4 of 1/((x-3)^{3/2)}	\int\:_{3}^{4}\frac{1}{(x-3)^{\frac{3}{2}}}dx
integral of 1/(1-sin(5x))	\int\:\frac{1}{1-\sin(5x)}dx
derivative of 16xsin(x)	\frac{d}{dx}(16x\sin(x))
integral of 1/((5x+3)^2)	\int\:\frac{1}{(5x+3)^{2}}dx
integral from 0 to 1 of (x-sqrt(x))/3	\int\:_{0}^{1}\frac{x-\sqrt{x}}{3}dx
integral of e^{ax}cos(x)	\int\:e^{ax}\cos(x)dx
integral of (x^2+2)/(x^3+6x)	\int\:\frac{x^{2}+2}{x^{3}+6x}dx
derivative of sqrt(2t)	derivative\:\sqrt{2t}
derivative of sec(pi/3)tan(pi/3)	derivative\:\sec(\frac{π}{3})\tan(\frac{π}{3})
(11x^2*y-13x)dy=-(11xy^2-13y)dx	(11x^{2}\cdot\:y-13x)dy=-(11xy^{2}-13y)dx
integral from 0 to 1 of (x^2+3)e^{-x}	\int\:_{0}^{1}(x^{2}+3)e^{-x}dx
integral of-ye^y	\int\:-ye^{y}dy
(\partial)/(\partial x)(x^2sqrt(y)+xy)	\frac{\partial\:}{\partial\:x}(x^{2}\sqrt{y}+xy)
integral from 0 to pi/2 of sin^4(x)	\int\:_{0}^{\frac{π}{2}}\sin^{4}(x)dx
integral of ((ln(x)-1))/(x^2)	\int\:\frac{(\ln(x)-1)}{x^{2}}dx
derivative of 9x^5	\frac{d}{dx}(9x^{5})
integral of (ln(17x))^2	\int\:(\ln(17x))^{2}dx
limit as x approaches infinity of 8/10	\lim\:_{x\to\:\infty\:}(\frac{8}{10})
derivative of f(x)=(x^2+5)/(x-2)	derivative\:f(x)=\frac{x^{2}+5}{x-2}
(dy)/(dx)= 1/x	\frac{dy}{dx}=\frac{1}{x}
limit as n approaches infinity of nx	\lim\:_{n\to\:\infty\:}(nx)
(dy)/(dt)+e^ty=2e^t	\frac{dy}{dt}+e^{t}y=2e^{t}
tangent of f(x)=x^2-2x,(3,3)	tangent\:f(x)=x^{2}-2x,(3,3)
limit as x approaches 0 of Inx^2-x^2	\lim\:_{x\to\:0}(Inx^{2}-x^{2})
tangent of f(x)=-x^2,(3,-9)	tangent\:f(x)=-x^{2},(3,-9)
(dx)/(dt)=-40.8x+0.6	\frac{dx}{dt}=-40.8x+0.6
limit as x approaches-infinity of (2)^x	\lim\:_{x\to\:-\infty\:}((2)^{x})
limit as x approaches infinity of 1,x	\lim\:_{x\to\:\infty\:}(1,x)
integral from 0 to 4 of xsqrt(21-x^2)	\int\:_{0}^{4}x\sqrt{21-x^{2}}dx
y^{''}+2y^'=2x+5-e^{-2x}	y^{\prime\:\prime\:}+2y^{\prime\:}=2x+5-e^{-2x}
derivative of 1-e^{-5x}	\frac{d}{dx}(1-e^{-5x})
x(dy)/(dx)=y^2-4	x\frac{dy}{dx}=y^{2}-4
xy^'+y=5xy^2,y(1)=3	xy^{\prime\:}+y=5xy^{2},y(1)=3
derivative of ((x-1)^3)/(x^2)	derivative\:\frac{(x-1)^{3}}{x^{2}}
integral of 4/(4+e^x)	\int\:\frac{4}{4+e^{x}}dx
d/(dt)(((2t+5)/(t^2+1))^4)	\frac{d}{dt}((\frac{2t+5}{t^{2}+1})^{4})
(\partial)/(\partial u)(1/(u^2+v^2))	\frac{\partial\:}{\partial\:u}(\frac{1}{u^{2}+v^{2}})
d/(dI)((100I)/(I^2+I+4))	\frac{d}{dI}(\frac{100I}{I^{2}+I+4})
integral of (y^6)/(2y^7+2)	\int\:\frac{y^{6}}{2y^{7}+2}dy
(d^2)/(dx^2)(cos(x)+sin(x)+1/2 x^2+1/x)	\frac{d^{2}}{dx^{2}}(\cos(x)+\sin(x)+\frac{1}{2}x^{2}+\frac{1}{x})
derivative of 2(sin(x)^2)	\frac{d}{dx}(2(\sin(x))^{2})
integral of (x^{3k})/(k!)	\int\:\frac{x^{3k}}{k!}dx
limit as x approaches 1/5 of 2+\|5x-1\|	\lim\:_{x\to\:\frac{1}{5}}(2+\left\|5x-1\right\|)
integral of 2e^y	\int\:2e^{y}dy
derivative of (5x^2-x+11)^{3/2}	derivative\:(5x^{2}-x+11)^{\frac{3}{2}}
4y^{''}-4y^'+y=16e^{t/2}	4y^{\prime\:\prime\:}-4y^{\prime\:}+y=16e^{\frac{t}{2}}
normal of f(x)=3e^x+2x,(0,3)	normal\:f(x)=3e^{x}+2x,(0,3)
limit as x approaches 0 of \| 1/(x^3)\|	\lim\:_{x\to\:0}(\left\|\frac{1}{x^{3}}\right\|)
limit as x approaches 0+of x^{17x}	\lim\:_{x\to\:0+}(x^{17x})
integral from 0 to 5 of xe^{-x^2}	\int\:_{0}^{5}xe^{-x^{2}}dx
integral of xcos(118x)	\int\:x\cos(118x)dx
integral from 0 to 1 of 9x^2(1-5x^3)^2	\int\:_{0}^{1}9x^{2}(1-5x^{3})^{2}dx
sum from n=1 to infinity of (n+1)/(2n-3)	\sum\:_{n=1}^{\infty\:}\frac{n+1}{2n-3}
integral from-1 to 1 of 1/(x^4)	\int\:_{-1}^{1}\frac{1}{x^{4}}dx
d/(dt)(4sin(3t))	\frac{d}{dt}(4\sin(3t))
integral from 0 to 1 of 1/(sqrt(x))	\int\:_{0}^{1}\frac{1}{\sqrt{x}}dx
integral of xcos((npix)/2)	\int\:x\cos(\frac{nπx}{2})dx
derivative of (-u^2+3)/((u^2+3)^2)	derivative\:\frac{-u^{2}+3}{(u^{2}+3)^{2}}
integral of 2cos(θ)cos^5(sin(θ))	\int\:2\cos(θ)\cos^{5}(\sin(θ))dθ
sum from n=0 to infinity of 4^{2n}	\sum\:_{n=0}^{\infty\:}4^{2n}
limit as x approaches 1 of 3x^3-5x^2+x+8	\lim\:_{x\to\:1}(3x^{3}-5x^{2}+x+8)
derivative of (3x^2+3x-1*(2x+3))	\frac{d}{dx}((3x^{2}+3x-1)\cdot\:(2x+3))
sum from n=1 to infinity of (1/2)^{-n}	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{-n}
laplacetransform 4t^2-5sin(3t)	laplacetransform\:4t^{2}-5\sin(3t)
tangent of f(x)=-3x^3-2x^2-1,\at x=-1	tangent\:f(x)=-3x^{3}-2x^{2}-1,\at\:x=-1
(\partial)/(\partial x)((xz)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{xz}{x^{2}+y^{2}})
integral of cos(3x)(2+sin(3x))^4	\int\:\cos(3x)(2+\sin(3x))^{4}dx
d/(da)(sin(a)+sin(2a))	\frac{d}{da}(\sin(a)+\sin(2a))
derivative of (23/(x^4))	\frac{d}{dx}(\frac{23}{x^{4}})
integral of 1/(tan(5θ))	\int\:\frac{1}{\tan(5θ)}dθ
f(x)=x^{1/2}	f(x)=x^{\frac{1}{2}}
integral from 1 to 2 of ln(x-1)	\int\:_{1}^{2}\ln(x-1)dx
f(x)=e^x-x	f(x)=e^{x}-x
integral of (cos(x/3))/(sin^4(x/3))	\int\:\frac{\cos(\frac{x}{3})}{\sin^{4}(\frac{x}{3})}dx
integral of e^{7x}cos(3x)	\int\:e^{7x}\cos(3x)dx
integral of (sin(x))^{1/2}cos(x)	\int\:(\sin(x))^{\frac{1}{2}}\cos(x)dx
1/4 y^{''}+y^'+y=x^2-4x	\frac{1}{4}y^{\prime\:\prime\:}+y^{\prime\:}+y=x^{2}-4x
y*y^'+36x=0	y\cdot\:y^{\prime\:}+36x=0
area y=sqrt(x),y= x/2	area\:y=\sqrt{x},y=\frac{x}{2}
derivative of ae^{-2x}	\frac{d}{dx}(ae^{-2x})
implicit (dy)/(dx),4x^2y^7-2x=x^5+4y^3	implicit\:\frac{dy}{dx},4x^{2}y^{7}-2x=x^{5}+4y^{3}
derivative of 4x(x^2-2^2)	\frac{d}{dx}(4x(x^{2}-2)^{2})
f(x)=e^x-1	f(x)=e^{x}-1
derivative of f(x)=sqrt(x^3-4)	derivative\:f(x)=\sqrt{x^{3}-4}
integral of (1-x-y)^2	\int\:(1-x-y)^{2}dy
integral of 1/(4y)	\int\:\frac{1}{4y}dy

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