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Popular Calculus Problems

xy^'-3y+24=0	xy^{\prime\:}-3y+24=0
(d^2)/(dx^2)(10^x)	\frac{d^{2}}{dx^{2}}(10^{x})
integral of 2/(xln(x))	\int\:\frac{2}{x\ln(x)}dx
implicit (dy)/(dx),xy-5y^2=6	implicit\:\frac{dy}{dx},xy-5y^{2}=6
integral of x^5sqrt(4+x^6)	\int\:x^{5}\sqrt{4+x^{6}}dx
integral of (x^2)/(x^2-6x+10)	\int\:\frac{x^{2}}{x^{2}-6x+10}dx
limit as x approaches 0+of 1/(5x)	\lim\:_{x\to\:0+}(\frac{1}{5x})
area y=x^3-2x+1,y=-2x,x=1	area\:y=x^{3}-2x+1,y=-2x,x=1
limit as x approaches 1 of [x]	\lim\:_{x\to\:1}([x])
d/(dt)(1)	\frac{d}{dt}(1)
integral of 8x-7	\int\:8x-7dx
integral of sin^3(2x+1)	\int\:\sin^{3}(2x+1)dx
integral from 0 to 0.5 of 12(1+2x^2)	\int\:_{0}^{0.5}12(1+2x^{2})dx
integral of 19x	\int\:19xdx
derivative of f(x)=((x-3)^2)/((x+9))	derivative\:f(x)=\frac{(x-3)^{2}}{(x+9)}
derivative of 8x+8x^{-1}	derivative\:8x+8x^{-1}
derivative of e^{-x/y}	\frac{d}{dx}(e^{-\frac{x}{y}})
derivative of 4/3 pix^3	\frac{d}{dx}(\frac{4}{3}pix^{3})
tangent of 3x^2,\at x=4	tangent\:3x^{2},\at\:x=4
limit as x approaches 5 of x	\lim\:_{x\to\:5}(x)
limit as t approaches+0 of 8/t-8/(t^2+t)	\lim\:_{t\to\:+0}(\frac{8}{t}-\frac{8}{t^{2}+t})
integral of \sqrt[6]{x}	\int\:\sqrt[6]{x}dx
integral of (x^2+3)sin(2x)	\int\:(x^{2}+3)\sin(2x)dx
derivative of-e^{-x}x+3e^{-x}	derivative\:-e^{-x}x+3e^{-x}
taylor x*cos(2x),1	taylor\:x\cdot\:\cos(2x),1
y^'+9tan(9x)=7cos(9x)	y^{\prime\:}+9\tan(9x)=7\cos(9x)
derivative of-xcos(x+sin(x))	\frac{d}{dx}(-x\cos(x)+\sin(x))
derivative of sqrt(x+\sqrt{x)}	derivative\:\sqrt{x+\sqrt{x}}
integral of 1/(x^3+x^2+x)	\int\:\frac{1}{x^{3}+x^{2}+x}dx
integral of x^2sqrt(1-x)	\int\:x^{2}\sqrt{1-x}dx
integral from pi/4 to pi of sin(θ)	\int\:_{\frac{π}{4}}^{π}\sin(θ)dθ
derivative of f(x)=3x+sqrt(x)	derivative\:f(x)=3x+\sqrt{x}
derivative of 1/2 x^4-2x^2	\frac{d}{dx}(\frac{1}{2}x^{4}-2x^{2})
derivative of ln(sqrt((5x+1/(x^2-3))))	\frac{d}{dx}(\ln(\sqrt{\frac{5x+1}{x^{2}-3}}))
limit as x approaches 3 of (x^3-9)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{3}-9}{x-3})
taylor x^3+2x+1,1	taylor\:x^{3}+2x+1,1
integral of (x^7)/7-(4x^5)/5+(x^2)/2+x+C	\int\:\frac{x^{7}}{7}-\frac{4x^{5}}{5}+\frac{x^{2}}{2}+x+Cdx
derivative of (8(2x)^4+5)^3	derivative\:(8(2x)^{4}+5)^{3}
integral from 1 to 3 of ()(2t^3+3t-1)	\int\:_{1}^{3}\frac{d}{dt}(2t^{3}+3t-1)dt
(\partial)/(\partial x)((x^p+y^p)^{1/p})	\frac{\partial\:}{\partial\:x}((x^{p}+y^{p})^{\frac{1}{p}})
derivative of 4sin(2x)	derivative\:4\sin(2x)
(\partial)/(\partial x)(3x+4y+4)	\frac{\partial\:}{\partial\:x}(3x+4y+4)
tangent of 1/(5+3x)	tangent\:\frac{1}{5+3x}
integral of (11x-3)/((2x-1)(x-3))	\int\:\frac{11x-3}{(2x-1)(x-3)}dx
(\partial)/(\partial x)((5xz)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{5xz}{x+y})
limit as x approaches 0 of (5x^2-6x)/x	\lim\:_{x\to\:0}(\frac{5x^{2}-6x}{x})
inverse oflaplace 1/((s+2)(s+1))	inverselaplace\:\frac{1}{(s+2)(s+1)}
derivative of (2x^2-7)^{-1}	derivative\:(2x^{2}-7)^{-1}
integral of 1/(xln(x^8))	\int\:\frac{1}{x\ln(x^{8})}dx
(dy)/(dx)=(6y^2+5x^2)/(xy)	\frac{dy}{dx}=\frac{6y^{2}+5x^{2}}{xy}
f(x)= 2/(x^3)	f(x)=\frac{2}{x^{3}}
integral of 1/(-2x^2+13x-15)	\int\:\frac{1}{-2x^{2}+13x-15}dx
derivative of (3x-1/(x^{2/3)})	\frac{d}{dx}(\frac{3x-1}{x^{\frac{2}{3}}})
integral of-e^xsin(x)	\int\:-e^{x}\sin(x)dx
(y-2x)y(dy)/(dx)=-x(y-2x)	(y-2x)y\frac{dy}{dx}=-x(y-2x)
integral of 1/((x^2-16)^3)	\int\:\frac{1}{(x^{2}-16)^{3}}dx
integral of (7x-2)/((x-2)(x+1))	\int\:\frac{7x-2}{(x-2)(x+1)}dx
taylor x/(x+1)	taylor\:\frac{x}{x+1}
integral of (x+2)/(x^2+4x)	\int\:\frac{x+2}{x^{2}+4x}dx
derivative of y=4^{-5x+2}	derivative\:y=4^{-5x+2}
derivative of 4sin(x^2)	\frac{d}{dx}(4\sin(x^{2}))
xy^'-2y=-2x^2+x+1	xy^{\prime\:}-2y=-2x^{2}+x+1
(dy)/(dt)+8ty=5t	\frac{dy}{dt}+8ty=5t
derivative of 3x+x^2-3x^3-x^4	\frac{d}{dx}(3x+x^{2}-3x^{3}-x^{4})
derivative of arccsc(-3t^2)	derivative\:\arccsc(-3t^{2})
derivative of y=e^{-5x}	derivative\:y=e^{-5x}
derivative of sqrt(x)-10\sqrt[3]{x}	\frac{d}{dx}(\sqrt{x}-10\sqrt[3]{x})
(\partial)/(\partial x)(x^2+y^2-xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-xy)
integral of 2e^x+8x^3+6x	\int\:2e^{x}+8x^{3}+6xdx
(dy)/(dx)+3y=8	\frac{dy}{dx}+3y=8
integral from 2 to 3 of 9/(sqrt(3-x))	\int\:_{2}^{3}\frac{9}{\sqrt{3-x}}dx
derivative of x^4-4x^3+10	\frac{d}{dx}(x^{4}-4x^{3}+10)
limit as x approaches 0 of 8e^xsin(x)	\lim\:_{x\to\:0}(8e^{x}\sin(x))
derivative of f(x)=x^2ln(x^3)	derivative\:f(x)=x^{2}\ln(x^{3})
1/4 y^{''}+10y^'+1000y=0	\frac{1}{4}y^{\prime\:\prime\:}+10y^{\prime\:}+1000y=0
derivative of ({f}(x)/(x^9))	\frac{d}{dx}(\frac{{f}(x)}{x^{9}})
tangent of f(x)=sqrt(x-3),\at x=19	tangent\:f(x)=\sqrt{x-3},\at\:x=19
integral of cos^2(x)-sin^2(x)	\int\:\cos^{2}(x)-\sin^{2}(x)dx
e^{2x}y^'-2y=3e^{4x}	e^{2x}y^{\prime\:}-2y=3e^{4x}
derivative of 5sec(8x)	derivative\:5\sec(8x)
(\partial)/(\partial x)(2y^2sin(xy))	\frac{\partial\:}{\partial\:x}(2y^{2}\sin(xy))
limit as t approaches 0 of tln(t)	\lim\:_{t\to\:0}(t\ln(t))
derivative of 90+45cos((x^2/(18)))	\frac{d}{dx}(90+45\cos(\frac{x^{2}}{18}))
(\partial)/(\partial y)(5xe^{x^2}+y^2)	\frac{\partial\:}{\partial\:y}(5xe^{x^{2}}+y^{2})
limit as x approaches 0 of (\|x^2-2x\|)/x	\lim\:_{x\to\:0}(\frac{\left\|x^{2}-2x\right\|}{x})
derivative of 3x^2-4	\frac{d}{dx}(3x^{2}-4)
derivative of arctan(1/x)	derivative\:\arctan(\frac{1}{x})
(\partial)/(\partial v)(sin(v))	\frac{\partial\:}{\partial\:v}(\sin(v))
taylor 1/(x+4),0	taylor\:\frac{1}{x+4},0
limit as (x,y,z) approaches (pi,0, 1/3) of e^{y^2}tan(xz)	\lim\:_{(x,y,z)\to\:(π,0,\frac{1}{3})}(e^{y^{2}}\tan(xz))
integral of sec^2(4x)	\int\:\sec^{2}(4x)dx
integral from-32 to 0 of 1/(sqrt(4-x))	\int\:_{-32}^{0}\frac{1}{\sqrt{4-x}}dx
derivative of (3cos(x)/(3x^3+2x^2-x+4))	\frac{d}{dx}(\frac{3\cos(x)}{3x^{3}+2x^{2}-x+4})
integral of 4cos^2(3x)	\int\:4\cos^{2}(3x)dx
integral of (-sin(3x))/(cos^3(3x))	\int\:\frac{-\sin(3x)}{\cos^{3}(3x)}dx
laplacetransform sin(2x)	laplacetransform\:\sin(2x)
derivative of sqrt(-2x^2+1)	\frac{d}{dx}(\sqrt{-2x^{2}+1})
limit as x approaches-3 of 4x^2	\lim\:_{x\to\:-3}(4x^{2})
derivative of 4csc(x)	\frac{d}{dx}(4\csc(x))
derivative of (x^{3/2}+2/x)	\frac{d}{dx}(\frac{x^{\frac{3}{2}}+2}{x})

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