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Popular Calculus Problems

derivative of sqrt(ax)	\frac{d}{dx}(\sqrt{ax})
sum from n=1 to infinity of nsin(npi)	\sum\:_{n=1}^{\infty\:}n\sin(nπ)
derivative of ((3x^2-2/(2x+3))^3)	\frac{d}{dx}((\frac{3x^{2}-2}{2x+3})^{3})
(\partial)/(\partial x)(3x^2-y^3+x-1)	\frac{\partial\:}{\partial\:x}(3x^{2}-y^{3}+x-1)
integral of ((ln(x^8)))/x	\int\:\frac{(\ln(x^{8}))}{x}dx
integral of sin(1/3)x	\int\:\sin(\frac{1}{3})xdx
(\partial)/(\partial x)(9ye^x-ln(z))	\frac{\partial\:}{\partial\:x}(9ye^{x}-\ln(z))
inverse oflaplace (s+2)/(s^2+2s+5)	inverselaplace\:\frac{s+2}{s^{2}+2s+5}
laplacetransform (t-2)e^{-4t}	laplacetransform\:(t-2)e^{-4t}
derivative of 4x+(144)/x+80	derivative\:4x+\frac{144}{x}+80
derivative of log_{e}(x^2+x+1)	\frac{d}{dx}(\log_{e}(x^{2}+x+1))
derivative of (-3x^5-3^3)	\frac{d}{dx}((-3x^{5}-3)^{3})
integral of x(1-x)^{2/3}	\int\:x(1-x)^{\frac{2}{3}}dx
limit as x approaches 0+of 2x^{3x}	\lim\:_{x\to\:0+}(2x^{3x})
derivative of 1/(x^3+4x^2)	\frac{d}{dx}(\frac{1}{x^{3}+4x^{2}})
derivative of x^2cos(x-2xsin(x)-2cos(x))	\frac{d}{dx}(x^{2}\cos(x)-2x\sin(x)-2\cos(x))
integral of 7tan^2(x)+tan^4(x)	\int\:7\tan^{2}(x)+\tan^{4}(x)dx
integral of 3x^3-5x^2+7x+2	\int\:3x^{3}-5x^{2}+7x+2dx
derivative of sqrt((5x+1/(2x^2+1)))	\frac{d}{dx}(\sqrt{\frac{5x+1}{2x^{2}+1}})
limit as x approaches infinity of (3x^2+2x-8)/(sqrt(4x^4-5x+4))	\lim\:_{x\to\:\infty\:}(\frac{3x^{2}+2x-8}{\sqrt{4x^{4}-5x+4}})
limit as x approaches 0 of 1/(sqrt(x+1))	\lim\:_{x\to\:0}(\frac{1}{\sqrt{x+1}})
integral of (1/3)x^3-5x	\int\:(\frac{1}{3})x^{3}-5xdx
derivative of 9e^{3x}x+6e^{3x}	\frac{d}{dx}(9e^{3x}x+6e^{3x})
integral of (6x^2-4x+5)	\int\:(6x^{2}-4x+5)dx
integral of 1/(x^3+9x)	\int\:\frac{1}{x^{3}+9x}dx
tangent of 5sec(x),\at x= pi/3	tangent\:5\sec(x),\at\:x=\frac{π}{3}
area-x^2+3x,2x^3-x^2-5x	area\:-x^{2}+3x,2x^{3}-x^{2}-5x
limit as x approaches 0 of ((x-1))/x	\lim\:_{x\to\:0}(\frac{(x-1)}{x})
integral of y/((y^2+z^2)^{3/2)}	\int\:\frac{y}{(y^{2}+z^{2})^{\frac{3}{2}}}dy
slope of (1,7),(7,3)	slope\:(1,7),(7,3)
d/(dθ)(4sin^2(θ)cos(θ))	\frac{d}{dθ}(4\sin^{2}(θ)\cos(θ))
derivative of (9(1-sin(x))/(2cos(x)))	\frac{d}{dx}(\frac{9(1-\sin(x))}{2\cos(x)})
d/(dy)(sqrt(y^2))	\frac{d}{dy}(\sqrt{y^{2}})
integral of 1/((xln(x)))	\int\:\frac{1}{(x\ln(x))}dx
integral of (8+3x)/(x(x^2+4))	\int\:\frac{8+3x}{x(x^{2}+4)}dx
derivative of x^3-15x^2+72x	derivative\:x^{3}-15x^{2}+72x
integral of 1/(\sqrt[3]{1+2x)}	\int\:\frac{1}{\sqrt[3]{1+2x}}dx
integral of 1/(sqrt(12x-x^2))	\int\:\frac{1}{\sqrt{12x-x^{2}}}dx
derivative of (ln(5x)/(5x))	\frac{d}{dx}(\frac{\ln(5x)}{5x})
taylor 1.5^x	taylor\:1.5^{x}
integral of x/(9-x^2)	\int\:\frac{x}{9-x^{2}}dx
integral of 1/(sin^2(3x))	\int\:\frac{1}{\sin^{2}(3x)}dx
(dy)/(dx)=(sec(y))/((x-3)^2)	\frac{dy}{dx}=\frac{\sec(y)}{(x-3)^{2}}
(dy)/(dx)-2xy=xy^2	\frac{dy}{dx}-2xy=xy^{2}
derivative of (7-sec(x))/(tan(x))	derivative\:\frac{7-\sec(x)}{\tan(x)}
integral from 0 to 1 of 8cos(x^2)	\int\:_{0}^{1}8\cos(x^{2})dx
tangent of f(x)=2+2e^{-x},\at x=ln(5)	tangent\:f(x)=2+2e^{-x},\at\:x=\ln(5)
derivative of 1/(6x^3)	derivative\:\frac{1}{6x^{3}}
integral of sin(x)cos^4(x)	\int\:\sin(x)\cos^{4}(x)dx
81y^{''}+180y^'+100y=0	81y^{\prime\:\prime\:}+180y^{\prime\:}+100y=0
integral from 0 to 20 of 3x	\int\:_{0}^{20}3xdx
integral of 1/(t^2sqrt(100-t^2))	\int\:\frac{1}{t^{2}\sqrt{100-t^{2}}}dt
limit as x approaches 0 of ln(cos(x))	\lim\:_{x\to\:0}(\ln(\cos(x)))
4ty^'+4=5+t	4ty^{\prime\:}+4=5+t
limit as x approaches 0 of 0^0	\lim\:_{x\to\:0}(0^{0})
derivative of f(x)=(x^2)/(x+3)	derivative\:f(x)=\frac{x^{2}}{x+3}
(\partial)/(\partial x)(4xy+3yz+5xy-48)	\frac{\partial\:}{\partial\:x}(4xy+3yz+5xy-48)
derivative of x^nln(1/x)	\frac{d}{dx}(x^{n}\ln(\frac{1}{x}))
inverse oflaplace (-3)/((s-2)^2)	inverselaplace\:\frac{-3}{(s-2)^{2}}
derivative of x^4-x^2	\frac{d}{dx}(x^{4}-x^{2})
integral of tan(5x)	\int\:\tan(5x)dx
derivative of (x^2-2x+5/(x^2+9))	\frac{d}{dx}(\frac{x^{2}-2x+5}{x^{2}+9})
integral of (-3/(sqrt(10-10x^2)))	\int\:(-\frac{3}{\sqrt{10-10x^{2}}})dx
y=3tan(2x)	y=3\tan(2x)
integral of (-6)/(x^2sqrt(x^2-9))	\int\:\frac{-6}{x^{2}\sqrt{x^{2}-9}}dx
derivative of 1/((1+x^2^{1/2)})	\frac{d}{dx}(\frac{1}{(1+x^{2})^{\frac{1}{2}}})
inverse oflaplace 5/(s^2+12)	inverselaplace\:\frac{5}{s^{2}+12}
integral of sin^3(2ax)cos(2ax)	\int\:\sin^{3}(2ax)\cos(2ax)dx
integral of (2x-3)/(x(2x+1)(2x-1))	\int\:\frac{2x-3}{x(2x+1)(2x-1)}dx
integral of (ln(x+1))/(x^2)	\int\:\frac{\ln(x+1)}{x^{2}}dx
(dy)/(dt)=y^3-y	\frac{dy}{dt}=y^{3}-y
integral of 1/(xsqrt(7x-1))	\int\:\frac{1}{x\sqrt{7x-1}}dx
derivative of e^{cos(2x})	\frac{d}{dx}(e^{\cos(2x)})
taylor cos(pi-4x)	taylor\:\cos(π-4x)
integral of 3/125 x^2	\int\:\frac{3}{125}x^{2}dx
limit as x approaches 0 of 4x	\lim\:_{x\to\:0}(4x)
integral of (3/(x^2)-2/(x^3))	\int\:(\frac{3}{x^{2}}-\frac{2}{x^{3}})dx
sum from n=1 to infinity of (n!)/(n*3^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n\cdot\:3^{n}}
area y=18sin(x),y=18cos(x)	area\:y=18\sin(x),y=18\cos(x)
area x^2-4x+3,-x^2+2x+3,4,0	area\:x^{2}-4x+3,-x^{2}+2x+3,4,0
t^2(dy)/(dt)-t=1+y+ty,y(1)=8	t^{2}\frac{dy}{dt}-t=1+y+ty,y(1)=8
derivative of y=(ln(6x))/(6x)	derivative\:y=\frac{\ln(6x)}{6x}
(d^2)/(dx^2)(\sqrt[11]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[11]{x})
sum from n=1 to infinity of 6/(n(n+2))	\sum\:_{n=1}^{\infty\:}\frac{6}{n(n+2)}
(dy)/(dx)=y^2	\frac{dy}{dx}=y^{2}
integral from 0 to 1 of (x^2+2)e^{-x}	\int\:_{0}^{1}(x^{2}+2)e^{-x}dx
(dy)/(dx)=sqrt(9y)e^{x+5}	\frac{dy}{dx}=\sqrt{9y}e^{x+5}
y^'=xsin(2y)	y^{\prime\:}=x\sin(2y)
integral from 2 to 5 of e^{2x}	\int\:_{2}^{5}e^{2x}dx
(\partial)/(\partial x)(4x^5-2y^{-3})	\frac{\partial\:}{\partial\:x}(4x^{5}-2y^{-3})
derivative of (9+2x-6sqrt(x))/x	derivative\:\frac{9+2x-6\sqrt{x}}{x}
y^{''}+y^'-2y=0	y^{\prime\:\prime\:}+y^{\prime\:}-2y=0
derivative of-x^4+50x^2-300	\frac{d}{dx}(-x^{4}+50x^{2}-300)
slope of (4.1)(7.1)	slope\:(4.1)(7.1)
integral from 2 to infinity of xe^{-5x}	\int\:_{2}^{\infty\:}xe^{-5x}dx
limit as x approaches 0+of tan(x^2)ln(x)	\lim\:_{x\to\:0+}(\tan(x^{2})\ln(x))
(dy)/(dx)-y=1	\frac{dy}{dx}-y=1
integral of sec(x/7)	\int\:\sec(\frac{x}{7})dx
integral from 5 to 6 of 1/((x-5)^{3/2)}	\int\:_{5}^{6}\frac{1}{(x-5)^{\frac{3}{2}}}dx
limit as x approaches 0 of (1-tan(kx))/x	\lim\:_{x\to\:0}(\frac{1-\tan(kx)}{x})

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