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Popular Calculus Problems

derivative of 4/(sqrt(sec(x)))	\frac{d}{dx}(\frac{4}{\sqrt{\sec(x)}})
integral from-1 to 5 of (1+4x)	\int\:_{-1}^{5}(1+4x)dx
y^{''}-4y^'+9y=xe^x	y^{\prime\:\prime\:}-4y^{\prime\:}+9y=xe^{x}
derivative of (2x^2^2)	\frac{d}{dx}((2x^{2})^{2})
derivative of f(x)=(10x+8x^2)/((5+8x)^2)	derivative\:f(x)=\frac{10x+8x^{2}}{(5+8x)^{2}}
area 4sqrt(x),2x	area\:4\sqrt{x},2x
derivative of f(x)=7e^xsqrt(x)	derivative\:f(x)=7e^{x}\sqrt{x}
integral of sin^2(3x)cos(3x)	\int\:\sin^{2}(3x)\cos(3x)dx
integral of x*cos(4x)	\int\:x\cdot\:\cos(4x)dx
y^'=sqrt(y)	y^{\prime\:}=\sqrt{y}
derivative of (4-x^2)/(x^3)	derivative\:\frac{4-x^{2}}{x^{3}}
derivative of sin(x-xsin(y))	\frac{d}{dx}(\sin(x)-x\sin(y))
limit as x approaches 4 of (2x+1)/(3x+3)	\lim\:_{x\to\:4}(\frac{2x+1}{3x+3})
(dy}{dx}=\frac{e^x)/y	\frac{dy}{dx}=\frac{e^{x}}{y}
integral from-infinity to 18 of xe^{x/9}	\int\:_{-\infty\:}^{18}xe^{\frac{x}{9}}dx
derivative of (x^2-10x+9sqrt(25-x^2))	\frac{d}{dx}((x^{2}-10x+9)\sqrt{25-x^{2}})
integral of (xcos^2(y)-sin(y))	\int\:(x\cos^{2}(y)-\sin(y))dx
integral of [cos(x/2)-sin(3 x/2)]	\int\:[\cos(\frac{x}{2})-\sin(3\frac{x}{2})]dx
derivative of 7/(x^{-2}+5/(x^{-3)})	\frac{d}{dx}(\frac{7}{x^{-2}}+\frac{5}{x^{-3}})
area sqrt(x), 1/3 x,x=25	area\:\sqrt{x},\frac{1}{3}x,x=25
limit as x approaches 0 of 100/2	\lim\:_{x\to\:0}(\frac{100}{2})
derivative of tan^4(3x^2)	\frac{d}{dx}(\tan^{4}(3)x^{2})
integral of ((x^2+x))/((x-3)(x^2+1))	\int\:\frac{(x^{2}+x)}{(x-3)(x^{2}+1)}dx
integral of-1/((x+3)^2)	\int\:-\frac{1}{(x+3)^{2}}dx
derivative of (x^2/(20))	\frac{d}{dx}(\frac{x^{2}}{20})
derivative of 3sqrt(x)-4x	\frac{d}{dx}(3\sqrt{x}-4x)
integral from 1 to 2 of x/(1+4x^2)	\int\:_{1}^{2}\frac{x}{1+4x^{2}}dx
slope of (-3/7 ,0),(0,6)	slope\:(-\frac{3}{7},0),(0,6)
integral from 0 to 5 of e^x	\int\:_{0}^{5}e^{x}dx
limit as x approaches 4 of 3x^5-4	\lim\:_{x\to\:4}(3x^{5}-4)
area sqrt(x),x-2,0,4	area\:\sqrt{x},x-2,0,4
inverse oflaplace s/((s+3)^2+1)	inverselaplace\:\frac{s}{(s+3)^{2}+1}
integral of (10)/(r^2)	\int\:\frac{10}{r^{2}}dr
6t(dy)/(dt)+y=t^3	6t\frac{dy}{dt}+y=t^{3}
derivative of x^2+4y^2	derivative\:x^{2}+4y^{2}
y^'=((3t^2-e^t))/(2y-5)	y^{\prime\:}=\frac{(3t^{2}-e^{t})}{2y-5}
limit as x approaches 5 of 2e^x-2ln(x)	\lim\:_{x\to\:5}(2e^{x}-2\ln(x))
d/(dt)(-2t)	\frac{d}{dt}(-2t)
integral of tan^2(1)	\int\:\tan^{2}(1)dx
area y=9x^2,x=1,y=0	area\:y=9x^{2},x=1,y=0
integral of \sqrt[3]{x^{10}}	\int\:\sqrt[3]{x^{10}}dx
(\partial)/(\partial y)(ln(x+2y+3z))	\frac{\partial\:}{\partial\:y}(\ln(x+2y+3z))
integral of n/(n^2+6n+10)	\int\:\frac{n}{n^{2}+6n+10}
integral of (4x-3)/(4x^2-6x)	\int\:\frac{4x-3}{4x^{2}-6x}dx
integral of ((x+1))/(x^2+2x)	\int\:\frac{(x+1)}{x^{2}+2x}dx
integral of tanh(x/6)	\int\:\tanh(\frac{x}{6})dx
limit as x approaches 0 of 2cos(1/x)	\lim\:_{x\to\:0}(2\cos(\frac{1}{x}))
tangent of y=x^3,\at x=-3	tangent\:y=x^{3},\at\:x=-3
derivative of y=(x^5)/(4-x^4)	derivative\:y=\frac{x^{5}}{4-x^{4}}
inverse oflaplace 2/(s(5s+1))	inverselaplace\:\frac{2}{s(5s+1)}
derivative of e^{-y^2}	derivative\:e^{-y^{2}}
integral of (8)	\int\:(8)dx
integral from 0 to pi of integral of 1	\int\:_{0}^{π}\int\:1dxdy
limit as x approaches infinity of x^{-5}	\lim\:_{x\to\:\infty\:}(x^{-5})
derivative of (768/(sqrt(x))-1)	\frac{d}{dx}(\frac{768}{\sqrt{x}}-1)
integral from-1 to 0 of 6(e^{1/x})/(x^3)	\int\:_{-1}^{0}6\frac{e^{\frac{1}{x}}}{x^{3}}dx
area 12-x-x^2,x+4	area\:12-x-x^{2},x+4
area y1=x^3+4x^2-6x-9,y2=3x^2	area\:y1=x^{3}+4x^{2}-6x-9,y2=3x^{2}
tangent of f(x)=e^{7x^2},\at x=2	tangent\:f(x)=e^{7x^{2}},\at\:x=2
integral of y-ye^z	\int\:y-ye^{z}dx
integral of r/((r^2+x^2)^{3/2)}	\int\:\frac{r}{(r^{2}+x^{2})^{\frac{3}{2}}}dr
limit as x approaches 6-of 5/(x-6)	\lim\:_{x\to\:6-}(\frac{5}{x-6})
(\partial)/(\partial y)(sqrt(1-x^2))	\frac{\partial\:}{\partial\:y}(\sqrt{1-x^{2}})
limit as x approaches 0+of x^{17}ln(x)	\lim\:_{x\to\:0+}(x^{17}\ln(x))
integral from 3 to 12 of ln(x^8)	\int\:_{3}^{12}\ln(x^{8})dx
y^'=-1/2 y	y^{\prime\:}=-\frac{1}{2}y
integral of ((12)/x+x/(12))	\int\:(\frac{12}{x}+\frac{x}{12})dx
xy^'+3y=(2e^{4x})/(x^2)	xy^{\prime\:}+3y=\frac{2e^{4x}}{x^{2}}
derivative of ax^2e^{-x}	\frac{d}{dx}(ax^{2}e^{-x})
derivative of ln(3/(x^2+9))	\frac{d}{dx}(\ln(\frac{3}{x^{2}+9}))
tangent of f(x)=x^x,\at x=2	tangent\:f(x)=x^{x},\at\:x=2
(xy^2-x)dx+(x^2y+y)dy=0	(xy^{2}-x)dx+(x^{2}y+y)dy=0
(\partial)/(\partial x)(20-2x+1.5-x+3x)	\frac{\partial\:}{\partial\:x}(20-2x+1.5-x+3x)
(d^2}{dx^2}(-8sin(\frac{3x)/2+1))	\frac{d^{2}}{dx^{2}}(-8\sin(\frac{3x}{2}+1))
(\partial)/(\partial t)(xe^{-t}sin(θ))	\frac{\partial\:}{\partial\:t}(xe^{-t}\sin(θ))
limit as x approaches 0+of 1/(x^2)+ln(x)	\lim\:_{x\to\:0+}(\frac{1}{x^{2}}+\ln(x))
integral of (-10)/(x^2(25-x^2)^{1/2)}	\int\:\frac{-10}{x^{2}(25-x^{2})^{\frac{1}{2}}}dx
tangent of sqrt(x)(x-8)	tangent\:\sqrt{x}(x-8)
integral of \sqrt[4]{x}	\int\:\sqrt[4]{x}dx
limit as x approaches 4 of (x^4-256)/(x^3-64)	\lim\:_{x\to\:4}(\frac{x^{4}-256}{x^{3}-64})
maclaurin (1+x^2)^{-3/2}	maclaurin\:(1+x^{2})^{-\frac{3}{2}}
area f(x)= 7/x ,x=1,x=41	area\:f(x)=\frac{7}{x},x=1,x=41
limit as x approaches 3+of (6x)/(x^2-9)	\lim\:_{x\to\:3+}(\frac{6x}{x^{2}-9})
laplacetransform tsin(t)	laplacetransform\:t\sin(t)
integral from 0 to infinity of x^2	\int\:_{0}^{\infty\:}x^{2}dx
integral of 1/(x^2+7)	\int\:\frac{1}{x^{2}+7}dx
derivative of arctan(x+x/(1+x^2))	\frac{d}{dx}(\arctan(x)+\frac{x}{1+x^{2}})
derivative of (tan(x))(sqrt(x))	derivative\:(\tan(x))(\sqrt{x})
(\partial)/(\partial x)(ln(2x+5y))	\frac{\partial\:}{\partial\:x}(\ln(2x+5y))
y^{''}+2y^'+3/4 y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+\frac{3}{4}y=0
integral of 3-1/(x^4)	\int\:3-\frac{1}{x^{4}}dx
(ln(1))^'	(\ln(1))^{\prime\:}
derivative of (sqrt(x)-7/(sqrt(x)+1))	\frac{d}{dx}(\frac{\sqrt{x}-7}{\sqrt{x}+1})
integral of 8cos^3(x)	\int\:8\cos^{3}(x)dx
(\partial)/(\partial x)(p(x))	\frac{\partial\:}{\partial\:x}(p(x))
derivative of x^2sin^4(x+xcos^{-2}(x))	\frac{d}{dx}(x^{2}\sin^{4}(x)+x\cos^{-2}(x))
y^'-6y=2e^t	y^{\prime\:}-6y=2e^{t}
y^{''}-4y^'+4y=0,y(0)=-4,y^'(0)=-6	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=0,y(0)=-4,y^{\prime\:}(0)=-6
limit as x approaches+2 of [7f(x)+g(x)]	\lim\:_{x\to\:+2}([7f(x)+g(x)])
y^'+e^ty=-17e^t	y^{\prime\:}+e^{t}y=-17e^{t}

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