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Popular Calculus Problems

slope ofintercept (0,9),(7,4)	slopeintercept\:(0,9),(7,4)
laplacetransform 6t^3e^{-2t}	laplacetransform\:6t^{3}e^{-2t}
integral of 1/((1+4x^2)(arctan(2x))^3)	\int\:\frac{1}{(1+4x^{2})(\arctan(2x))^{3}}dx
integral of sin^4(6x)	\int\:\sin^{4}(6x)dx
limit as x approaches 0+of 3x^{sqrt(x)}	\lim\:_{x\to\:0+}(3x^{\sqrt{x}})
2x^2y^{''}+6xy^'+2y=0,y(1)=2,y^'(1)=-1	2x^{2}y^{\prime\:\prime\:}+6xy^{\prime\:}+2y=0,y(1)=2,y^{\prime\:}(1)=-1
y^{''}-6y^'+9y=2te^{3t}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=2te^{3t}
limit as x approaches 2-of 4/((x-2)^5)	\lim\:_{x\to\:2-}(\frac{4}{(x-2)^{5}})
y^'-y=4sin(3t)	y^{\prime\:}-y=4\sin(3t)
inverse oflaplace 1/(s-1)	inverselaplace\:\frac{1}{s-1}
sum from n=4 to infinity of 1/((n)(n+1))	\sum\:_{n=4}^{\infty\:}\frac{1}{(n)(n+1)}
integral from 0 to x of 1/((1-x))	\int\:_{0}^{x}\frac{1}{(1-x)}dx
limit as x approaches 0 of 1/(1-e^x)	\lim\:_{x\to\:0}(\frac{1}{1-e^{x}})
sum from n=1 to infinity of (cos(32))^n	\sum\:_{n=1}^{\infty\:}(\cos(32))^{n}
(\partial)/(\partial x)(x^3-9xy+7y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-9xy+7y^{3})
derivative of 750+12x-0.8x^7	\frac{d}{dx}(750+12x-0.8x^{7})
maclaurin cos(x^4)	maclaurin\:\cos(x^{4})
derivative of x*e^{-x}	derivative\:x\cdot\:e^{-x}
derivative of (3+x/(1-3x))	\frac{d}{dx}(\frac{3+x}{1-3x})
area y=(4x)/(1+x^2),y=(4x^2)/(1+x^3)	area\:y=\frac{4x}{1+x^{2}},y=\frac{4x^{2}}{1+x^{3}}
(\partial)/(\partial x)(4ax^4+7b(x,t)t^3)	\frac{\partial\:}{\partial\:x}(4ax^{4}+7b(x,t)t^{3})
derivative of y=(4+xf(x))/(sqrt(x))	derivative\:y=\frac{4+xf(x)}{\sqrt{x}}
integral of xe^{-2}+ex^{-2}	\int\:xe^{-2}+ex^{-2}dx
(\partial)/(\partial z)(xy^2z^3)	\frac{\partial\:}{\partial\:z}(xy^{2}z^{3})
derivative of arctan((x-1)/(x+1))	derivative\:\arctan(\frac{x-1}{x+1})
derivative of ln(sin(x))	derivative\:\ln(\sin(x))
y^'=yx^2	y^{\prime\:}=yx^{2}
laplacetransform t^3cos(3t)	laplacetransform\:t^{3}\cos(3t)
derivative of sqrt(1+(x^2))	\frac{d}{dx}(\sqrt{1+(x)^{2}})
integral of x9^x	\int\:x9^{x}dx
integral of 1/(sqrt(26-x^2))	\int\:\frac{1}{\sqrt{26-x^{2}}}dx
derivative of (4x+2/(x+1))	\frac{d}{dx}(\frac{4x+2}{x+1})
integral of tan^5(5x)	\int\:\tan^{5}(5x)dx
integral of e/x+x/e	\int\:\frac{e}{x}+\frac{x}{e}dx
integral of sec^2(x)cos(x)	\int\:\sec^{2}(x)\cos(x)dx
area y=x^2-1,y=x+1	area\:y=x^{2}-1,y=x+1
integral from 1.5 to 2 of (2x)/3	\int\:_{1.5}^{2}\frac{2x}{3}dx
4y^{''}+10y=0	4y^{\prime\:\prime\:}+10y=0
limit as x approaches 2-of sqrt(x-2)	\lim\:_{x\to\:2-}(\sqrt{x-2})
integral of 28x(7x^2-5)^3	\int\:28x(7x^{2}-5)^{3}dx
integral of ae^{-at}	\int\:ae^{-at}dt
derivative of 3x^2e^x+e^x(x^3+4)	derivative\:3x^{2}e^{x}+e^{x}(x^{3}+4)
integral of x^5e^{x^6}	\int\:x^{5}e^{x^{6}}dx
slope of (-3.5)(2.1)	slope\:(-3.5)(2.1)
integral from 0 to 2 of x/2	\int\:_{0}^{2}\frac{x}{2}dx
(\partial)/(\partial x)(e^{-2x}sin(2x))	\frac{\partial\:}{\partial\:x}(e^{-2x}\sin(2x))
inverse oflaplace ((-2s+24))/((s^2-13))	inverselaplace\:\frac{(-2s+24)}{(s^{2}-13)}
integral of 9tan(x)sec^3(x)	\int\:9\tan(x)\sec^{3}(x)dx
integral of sin(2x)(e^{1+cos^2(x)})+3	\int\:\sin(2x)(e^{1+\cos^{2}(x)})+3dx
integral of cos^4(θ)	\int\:\cos^{4}(θ)dθ
derivative of 6sqrt(x^3)	\frac{d}{dx}(6\sqrt{x^{3}})
2xy(dy)/(dx)=x^2+2y^2	2xy\frac{dy}{dx}=x^{2}+2y^{2}
integral of sin(1/x)	\int\:\sin(\frac{1}{x})dx
f(x)=cot^3(x)	f(x)=\cot^{3}(x)
area y=sqrt(2x),y=3x-4,y=0	area\:y=\sqrt{2x},y=3x-4,y=0
limit as x approaches 2 of (2x)/(3x+1)	\lim\:_{x\to\:2}(\frac{2x}{3x+1})
(\partial)/(\partial y)(y^3cos(2x))	\frac{\partial\:}{\partial\:y}(y^{3}\cos(2x))
sum from k=1 to infinity}((-1)^k(1)^{(3k) of)/k	\sum\:_{k=1}^{\infty\:}\frac{(-1)^{k}\cdot\:(1)^{(3\cdot\:k)}}{k}
integral of xy(x+y)	\int\:xy(x+y)dy
sum from n=0 to infinity of (2^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{2^{n}}{n!}
integral of (x+2)sqrt(x-2)	\int\:(x+2)\sqrt{x-2}dx
integral of 1/((x^4-1))	\int\:\frac{1}{(x^{4}-1)}dx
integral from 2 to 1/x of tan^2(t)	\int\:_{2}^{\frac{1}{x}}\tan^{2}(t)dt
tangent of f(x)=x*cot(x),\at x= pi/4	tangent\:f(x)=x\cdot\:\cot(x),\at\:x=\frac{π}{4}
derivative of f(x)=(x+sqrt(x))/(x^3)	derivative\:f(x)=\frac{x+\sqrt{x}}{x^{3}}
derivative of y/(y+x^2)	\frac{d}{dx}(\frac{y}{y+x^{2}})
derivative of e^{x^2}sin(x)	\frac{d}{dx}(e^{x^{2}}\sin(x))
(dx)/(dt)=2x(10-x)	\frac{dx}{dt}=2x(10-x)
(\partial)/(\partial t)(e^tsin(t))	\frac{\partial\:}{\partial\:t}(e^{t}\sin(t))
derivative of 3ln(4x)	\frac{d}{dx}(3\ln(4x))
integral from 1 to 3 of (4x-3)^2-(x^2)^2	\int\:_{1}^{3}(4x-3)^{2}-(x^{2})^{2}dx
integral of (6x^2+8)/(x^3+4x)	\int\:\frac{6x^{2}+8}{x^{3}+4x}dx
(dy)/(dx)+y=e^{7x}	\frac{dy}{dx}+y=e^{7x}
y^'-5/x y=(y^5)/(x^{18)}	y^{\prime\:}-\frac{5}{x}y=\frac{y^{5}}{x^{18}}
integral from 9 to 16 of 1/(7-sqrt(x))	\int\:_{9}^{16}\frac{1}{7-\sqrt{x}}dx
integral of (sqrt(x))/(x-16)	\int\:\frac{\sqrt{x}}{x-16}dx
sum from n=0 to infinity of n^2(x)^{n-1}	\sum\:_{n=0}^{\infty\:}n^{2}(x)^{n-1}
laplacetransform 5t^4	laplacetransform\:5t^{4}
x^7y^'=-8x^6y+cos(2x)	x^{7}y^{\prime\:}=-8x^{6}y+\cos(2x)
integral of (-2ax)/(x^2+y^2)	\int\:\frac{-2ax}{x^{2}+y^{2}}dy
derivative of 1/2 x^2+x^{-1}	\frac{d}{dx}(\frac{1}{2}x^{2}+x^{-1})
integral of sqrt(x^2-4x)	\int\:\sqrt{x^{2}-4x}dx
integral from 1 to 3 of 3r^3ln(r)	\int\:_{1}^{3}3r^{3}\ln(r)dr
integral of (7x-11)^4	\int\:(7x-11)^{4}dx
y^{''}-3y^'+2y=2t^3	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=2t^{3}
derivative of ln(x^4-6x^2)	\frac{d}{dx}(\ln(x^{4}-6x^{2}))
integral of tan^3(21pix)	\int\:\tan^{3}(21πx)dx
derivative of g(x)=(sin(8x))/(cos(x))	derivative\:g(x)=\frac{\sin(8x)}{\cos(x)}
integral from 1 to infinity of-1/x	\int\:_{1}^{\infty\:}-\frac{1}{x}dx
(cos(3x))y^'-3(tan(3x))y=-10sec(3x)	(\cos(3x))y^{\prime\:}-3(\tan(3x))y=-10\sec(3x)
derivative of (t+1)cos(-t)	derivative\:(t+1)\cos(-t)
integral of-2cos^2(x)sin(x)	\int\:-2\cos^{2}(x)\sin(x)dx
(dv)/(dt)=32-4/5 v	\frac{dv}{dt}=32-\frac{4}{5}v
(\partial)/(\partial x)(x^5y^5+4x^7y)	\frac{\partial\:}{\partial\:x}(x^{5}y^{5}+4x^{7}y)
integral of 1/((x-5)^{3/2)}	\int\:\frac{1}{(x-5)^{\frac{3}{2}}}dx
xy^'+(1+2x)y=10e^{-2x}	xy^{\prime\:}+(1+2x)y=10e^{-2x}
limit as x approaches+1 of+(1/(x^2-1))	\lim\:_{x\to\:+1}(+(\frac{1}{x^{2}-1}))
integral from 0 to 6 of 1/(36+x^2)	\int\:_{0}^{6}\frac{1}{36+x^{2}}dx
derivative of x/((2x+3)^3)	derivative\:\frac{x}{(2x+3)^{3}}
(\partial)/(\partial x)(10x^{0.5})	\frac{\partial\:}{\partial\:x}(10x^{0.5})

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