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Popular Calculus Problems

(dy)/(dx)= 1/2 x+3	\frac{dy}{dx}=\frac{1}{2}x+3
integral of tan^5(x)sec^{-3/2}(x)	\int\:\tan^{5}(x)\sec^{-\frac{3}{2}}(x)dx
integral of x^2sqrt(x^2+9)	\int\:x^{2}\sqrt{x^{2}+9}dx
integral of 1/((5x)^2)	\int\:\frac{1}{(5x)^{2}}dx
integral of (ln(cos(x)))/((cos(x))^2)	\int\:\frac{\ln(\cos(x))}{(\cos(x))^{2}}dx
integral from-infinity to 0 of 2^r	\int\:_{-\infty\:}^{0}2^{r}dr
integral of (-9x+3)^4	\int\:(-9x+3)^{4}dx
derivative of 30e^x+x^{20}	derivative\:30e^{x}+x^{20}
integral of (x^2+x+3)/(x^4+6x^2+9)	\int\:\frac{x^{2}+x+3}{x^{4}+6x^{2}+9}dx
integral of 1/(-x^2)	\int\:\frac{1}{-x^{2}}dx
derivative of (x^2-6x+5/(x^2+7))	\frac{d}{dx}(\frac{x^{2}-6x+5}{x^{2}+7})
integral from 0 to 3 of (3x^2+x-2)	\int\:_{0}^{3}(3x^{2}+x-2)dx
integral of sqrt(x^3)+\sqrt[3]{x^2}	\int\:\sqrt{x^{3}}+\sqrt[3]{x^{2}}dx
y^{''}-4y^'+4y=5t^{-1}e^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=5t^{-1}e^{2t}
derivative of x^{ex}	\frac{d}{dx}(x^{ex})
(\partial)/(\partial x)(x^2(x-y)^{-2})	\frac{\partial\:}{\partial\:x}(x^{2}(x-y)^{-2})
derivative of 1/(3(x+2^{2/3)})	\frac{d}{dx}(\frac{1}{3(x+2)^{\frac{2}{3}}})
derivative of f(x)=(2x^2+1)	derivative\:f(x)=(2x^{2}+1)
integral of x^2sin(y)	\int\:x^{2}\sin(y)dy
integral of sin(6x)ln(sin(6x))	\int\:\sin(6x)\ln(\sin(6x))dx
integral of (x^2)/((36-x^2)^{3/2)}	\int\:\frac{x^{2}}{(36-x^{2})^{\frac{3}{2}}}dx
integral from 0 to sqrt(pi of)xcos(x^2)	\int\:_{0}^{\sqrt{π}}x\cos(x^{2})dx
t^3y^'+4t^2y=e^{-t}	t^{3}y^{\prime\:}+4t^{2}y=e^{-t}
sum from n=1 to infinity of 1/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{1}{(n+1)!}
integral of 2y+xe^{xy}	\int\:2y+xe^{xy}dy
derivative of 1/((x+3^5))	\frac{d}{dx}(\frac{1}{(x+3)^{5}})
y^{''}+2y^'+6y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+6y=0,y(0)=1,y^{\prime\:}(0)=0
limit as x approaches 0 of xsin(7/x)	\lim\:_{x\to\:0}(x\sin(\frac{7}{x}))
laplacetransform 8e^{pi-t}	laplacetransform\:8e^{π-t}
integral of sin(8x)cos(12x)	\int\:\sin(8x)\cos(12x)dx
(dy}{dx}=-\frac{xe^{-x^2})/y	\frac{dy}{dx}=-\frac{xe^{-x^{2}}}{y}
integral of 1/(e^{2t)}	\int\:\frac{1}{e^{2t}}dt
integral of (x-1)sqrt(x^2-2x)	\int\:(x-1)\sqrt{x^{2}-2x}dx
taylor (1+x/2)^{-4}	taylor\:(1+\frac{x}{2})^{-4}
3x^2y^{''}+7xy^'+y=24x+2	3x^{2}y^{\prime\:\prime\:}+7xy^{\prime\:}+y=24x+2
derivative of (x-11/(sqrt(x)-\sqrt{11)})	\frac{d}{dx}(\frac{x-11}{\sqrt{x}-\sqrt{11}})
integral of 1/(1+2e^x-e^{-x)}	\int\:\frac{1}{1+2e^{x}-e^{-x}}dx
derivative of (3x+5)^7	derivative\:(3x+5)^{7}
y^'-y/((100+4t))=150	y^{\prime\:}-\frac{y}{(100+4t)}=150
slope ofintercept (-2,-5),(-4,4)	slopeintercept\:(-2,-5),(-4,4)
limit as x approaches 4 of x^4e^{-x^3}	\lim\:_{x\to\:4}(x^{4}e^{-x^{3}})
limit as x approaches 1+of (ln(x))^{1-x}	\lim\:_{x\to\:1+}((\ln(x))^{1-x})
integral of (x-1)sqrt(1+e^{2y)}	\int\:(x-1)\sqrt{1+e^{2y}}dy
5x^{''}+50x=10	5x^{\prime\:\prime\:}+50x=10
integral of x(5x^2+2/3)^4	\int\:x(5x^{2}+\frac{2}{3})^{4}dx
derivative of-5x^3+x^2-3x-3	\frac{d}{dx}(-5x^{3}+x^{2}-3x-3)
derivative of (cos(x)/(1+cotan(x)))	\frac{d}{dx}(\frac{\cos(x)}{1+co\tan(x)})
derivative of x(a+bxe^{3x})	\frac{d}{dx}(x(a+bx)e^{3x})
derivative of e^{-1/(x^3})	\frac{d}{dx}(e^{-\frac{1}{x^{3}}})
integral of 6x^5e^{7x^6}	\int\:6x^{5}e^{7x^{6}}dx
derivative of x^{2/3}(6-x^{1/3})	\frac{d}{dx}(x^{\frac{2}{3}}(6-x)^{\frac{1}{3}})
y^{''}-3y^'+2y=4e^{2t}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=4e^{2t}
derivative of sqrt(-3x+7)	\frac{d}{dx}(\sqrt{-3x+7})
(\partial)/(\partial x)(3e^{xy+4})	\frac{\partial\:}{\partial\:x}(3e^{xy+4})
(dy)/(dx)=xy+5x+2y+10	\frac{dy}{dx}=xy+5x+2y+10
laplacetransform 13sin(2t)	laplacetransform\:13\sin(2t)
integral of ((10)/(1-sin^2(x)))	\int\:(\frac{10}{1-\sin^{2}(x)})dx
sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3))	\sum\:_{n=1}^{\infty\:}\frac{((-1)^{(n-1)})}{(n^{3})}
y^'+2y=3	y^{\prime\:}+2y=3
limit as x approaches 2-of sqrt(2-x)	\lim\:_{x\to\:2-}(\sqrt{2-x})
limit as x approaches 2-of 1/(x-2)	\lim\:_{x\to\:2-}(\frac{1}{x-2})
tangent of f(x)=2sqrt(x),\at x=1	tangent\:f(x)=2\sqrt{x},\at\:x=1
f(x)=(ln(x))^6	f(x)=(\ln(x))^{6}
derivative of 1/((x-3^2))	\frac{d}{dx}(\frac{1}{(x-3)^{2}})
integral of 1/(sqrt(49x^2-64))	\int\:\frac{1}{\sqrt{49x^{2}-64}}dx
derivative of-bsin(x)	\frac{d}{dx}(-b\sin(x))
tangent of x^6+y^2=2,(1,-1)	tangent\:x^{6}+y^{2}=2,(1,-1)
xy^'+2y=3cos(x)	xy^{\prime\:}+2y=3\cos(x)
slope of h(x)=4^x-6	slope\:h(x)=4^{x}-6
derivative of g(x)=3x^2cos(x)+8x	derivative\:g(x)=3x^{2}\cos(x)+8x
integral of x/((x^2+9))	\int\:\frac{x}{(x^{2}+9)}dx
laplacetransform x-5	laplacetransform\:x-5
integral of g/(1/p-\frac{gz){k}}	\int\:\frac{g}{\frac{1}{p}-\frac{gz}{k}}dz
tangent of f(x)= 1/(x^2),\at x=2	tangent\:f(x)=\frac{1}{x^{2}},\at\:x=2
integral of \sqrt[6]{x}+1/(\sqrt[6]{x)}	\int\:\sqrt[6]{x}+\frac{1}{\sqrt[6]{x}}dx
integral of u^3	\int\:u^{3}du
derivative of (2x-1)/(4x+8)	derivative\:\frac{2x-1}{4x+8}
integral of (ln(x^4))/x	\int\:\frac{\ln(x^{4})}{x}dx
derivative of 1/x e^x	\frac{d}{dx}(\frac{1}{x}e^{x})
(dy)/(dx)=a*y	\frac{dy}{dx}=a\cdot\:y
(e^{f(x)})\prime	(e^{f(x)})\prime
derivative of ((x^2+2x/(x+1))^5)	\frac{d}{dx}((\frac{x^{2}+2x}{x+1})^{5})
2y^'=3xy+1	2y^{\prime\:}=3xy+1
limit as x approaches 1 of (x^2-2x+1)cos(e^{1/(x-1)})	\lim\:_{x\to\:1}((x^{2}-2x+1)\cos(e^{\frac{1}{x-1}}))
limit as x approaches infinity of [2,x]	\lim\:_{x\to\:\infty\:}([2,x])
integral of (sin^2(x)-cos^2(x))	\int\:(\sin^{2}(x)-\cos^{2}(x))dx
(d^5)/(dx^5)(1/x)	\frac{d^{5}}{dx^{5}}(\frac{1}{x})
integral of e^xcot(e^x)	\int\:e^{x}\cot(e^{x})dx
limit as x approaches-6-of (-8x)/(x+6)	\lim\:_{x\to\:-6-}(\frac{-8x}{x+6})
integral of (sin(x))/(1-cos^2(x))	\int\:\frac{\sin(x)}{1-\cos^{2}(x)}dx
integral of sin(10x)ln(sin(10x))	\int\:\sin(10x)\ln(\sin(10x))dx
integral of xsqrt(3x^2-2)	\int\:x\sqrt{3x^{2}-2}dx
integral of tsin(t^2)	\int\:t\sin(t^{2})dt
limit as x approaches 2 of (4-2x)/(x-2)	\lim\:_{x\to\:2}(\frac{4-2x}{x-2})
roots ce^x	roots\:ce^{x}
3ydy=(2sin(2x)-e^x)ydx	3ydy=(2\sin(2x)-e^{x})ydx
(\partial)/(\partial x)(3x^6y^2)	\frac{\partial\:}{\partial\:x}(3x^{6}y^{2})
derivative of-5(2x-100^6)	\frac{d}{dx}(-5(2x-100)^{6})
d/(dt)(6t^2-8+40cos(pit))	\frac{d}{dt}(6t^{2}-8+40\cos(πt))
integral of 3t^4	\int\:3t^{4}dt

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