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Popular Calculus Problems

limit as x approaches 0+of x^{8x}	\lim\:_{x\to\:0+}(x^{8x})
derivative of 3/(x-4)	derivative\:\frac{3}{x-4}
d/(dt)(9tsin(pit))	\frac{d}{dt}(9t\sin(πt))
integral of x^3sqrt(x^2-3)	\int\:x^{3}\sqrt{x^{2}-3}dx
limit as x approaches infinity of 8xe^{1/x}-8x	\lim\:_{x\to\:\infty\:}(8xe^{\frac{1}{x}}-8x)
integral of (x^2+x)^7(2x+1)	\int\:(x^{2}+x)^{7}(2x+1)dx
integral from 0 to 1 of e^x-e^{-x}	\int\:_{0}^{1}e^{x}-e^{-x}dx
tangent of f(x)=e^x(9-3x+2x^2),\at x=0	tangent\:f(x)=e^{x}(9-3x+2x^{2}),\at\:x=0
integral of (e^{4x})/(1+e^x)	\int\:\frac{e^{4x}}{1+e^{x}}dx
integral of t(1-ln^2(t))	\int\:t(1-\ln^{2}(t))dt
integral of (-2sin(x)+4cos(x))	\int\:(-2\sin(x)+4\cos(x))dx
integral of xe^{-(x+y)}	\int\:xe^{-(x+y)}dx
derivative of (7-3x(x+5))	\frac{d}{dx}((7-3x)(x+5))
y^'+3y=cos(x)	y^{\prime\:}+3y=\cos(x)
4y^{''}+y^'+8y=0	4y^{\prime\:\prime\:}+y^{\prime\:}+8y=0
derivative of sqrt(x)+1/(x^2+x^3)	\frac{d}{dx}(\sqrt{x}+\frac{1}{x^{2}}+x^{3})
limit as x approaches 5 of 5+x^4	\lim\:_{x\to\:5}(5+x^{4})
integral of e^{-st}(t)	\int\:e^{-st}(t)dt
integral of (x^{3/2}+2x^6+1.2)/x	\int\:\frac{x^{\frac{3}{2}}+2x^{6}+1.2}{x}dx
derivative of cos(arctan(3x)-arcsin(2x))	derivative\:\cos(\arctan(3x)-\arcsin(2x))
derivative of 6*5^x	\frac{d}{dx}(6\cdot\:5^{x})
derivative of sin(tan(sqrt(1+x^3)))	\frac{d}{dx}(\sin(\tan(\sqrt{1+x^{3}})))
(dx)/(dy)=1+x^2	\frac{dx}{dy}=1+x^{2}
integral of (e^{-x})/(1-e^{-x)}	\int\:\frac{e^{-x}}{1-e^{-x}}dx
(\partial)/(\partial x)(x^3y^4sin^2(xy))	\frac{\partial\:}{\partial\:x}(x^{3}y^{4}\sin^{2}(xy))
integral of e^{(x^3)}	\int\:e^{(x^{3})}dx
integral of 1/((t^2+1)^2)	\int\:\frac{1}{(t^{2}+1)^{2}}dt
integral of x/(sqrt(x-2))	\int\:\frac{x}{\sqrt{x-2}}dx
derivative of 3/(2sqrt(x-8))	\frac{d}{dx}(\frac{3}{2\sqrt{x-8}})
integral of 1-2sin(x)	\int\:1-2\sin(x)dx
integral of (1/(2x^3)-1/(x^4))	\int\:(\frac{1}{2x^{3}}-\frac{1}{x^{4}})dx
(\partial)/(\partial x)(ln(xy^2))	\frac{\partial\:}{\partial\:x}(\ln(xy^{2}))
(\partial)/(\partial x)(e^{-x}sin(x^2+xy))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(x^{2}+xy))
(\partial)/(\partial u)(u^2-v^2)	\frac{\partial\:}{\partial\:u}(u^{2}-v^{2})
integral of csc^2(1/3)x	\int\:\csc^{2}(\frac{1}{3})xdx
derivative of 1/(1+t)	derivative\:\frac{1}{1+t}
derivative of (2x)/(x^4+1)	derivative\:\frac{2x}{x^{4}+1}
derivative of x^3-3x^2+3x-3	\frac{d}{dx}(x^{3}-3x^{2}+3x-3)
limit as x approaches 0+of (1+4x)^{5/x}	\lim\:_{x\to\:0+}((1+4x)^{\frac{5}{x}})
implicit (dy)/(dx),y^5=x^7	implicit\:\frac{dy}{dx},y^{5}=x^{7}
derivative of x^2+3x+1/(x^2)	derivative\:x^{2}+3x+\frac{1}{x^{2}}
integral of (arcsin(4x))/(sqrt(1-16x^2))	\int\:\frac{\arcsin(4x)}{\sqrt{1-16x^{2}}}dx
d/(d{r)}(sqrt({r)}+\sqrt[7]{{r}})	\frac{d}{d{r}}(\sqrt{{r}}+\sqrt[7]{{r}})
tangent of (x^2)/(7+sqrt(x))	tangent\:\frac{x^{2}}{7+\sqrt{x}}
derivative of x(3x+5^3)	\frac{d}{dx}(x(3x+5)^{3})
integral of x(3+x^2)^{10}	\int\:x(3+x^{2})^{10}dx
integral of (1/x+cot(x))	\int\:(\frac{1}{x}+\cot(x))dx
integral of 5/(x^2-4x+8)	\int\:\frac{5}{x^{2}-4x+8}dx
laplacetransform 8^t	laplacetransform\:8^{t}
limit as x approaches 2 of 9	\lim\:_{x\to\:2}(9)
slope of (1,0.5),(3,0)	slope\:(1,0.5),(3,0)
integral of sqrt(x^2-64)	\int\:\sqrt{x^{2}-64}dx
d/(da)((pi(9a^2+6a+1))/(54a))	\frac{d}{da}(\frac{π(9a^{2}+6a+1)}{54a})
integral of (e^x)/(sqrt(e^{2x)-2)}	\int\:\frac{e^{x}}{\sqrt{e^{2x}-2}}dx
limit as x approaches pi of (pi-x)csc(x)	\lim\:_{x\to\:π}((π-x)\csc(x))
9xy^2-3+(9x^2y+4)(dy)/(dx)=0	9xy^{2}-3+(9x^{2}y+4)\frac{dy}{dx}=0
(dy)/(dx)+4y=6	\frac{dy}{dx}+4y=6
integral of (x-2)^{-3}	\int\:(x-2)^{-3}dx
(\partial)/(\partial y)(2)	\frac{\partial\:}{\partial\:y}(2)
derivative of (xy^{1/2})	\frac{d}{dx}((xy)^{\frac{1}{2}})
limit as x approaches 0 of (tan(x))/(6x)	\lim\:_{x\to\:0}(\frac{\tan(x)}{6x})
laplacetransform-5cos(5t)	laplacetransform\:-5\cos(5t)
xy(dy)/(dx)=x^2-y^2	xy\frac{dy}{dx}=x^{2}-y^{2}
tangent of f(x)=sqrt(x+5),\at x=4	tangent\:f(x)=\sqrt{x+5},\at\:x=4
(2x-y)dx+(2y-x)dy=0	(2x-y)dx+(2y-x)dy=0
derivative of (1-x^{-2})	\frac{d}{dx}((1-x)^{-2})
y^'= y/x+1	y^{\prime\:}=\frac{y}{x}+1
y^{'''}+2y^{''}-5y^'-6y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-5y^{\prime\:}-6y=0
integral from 0 to pi of 16sin(x)	\int\:_{0}^{π}16\sin(x)dx
y^{''}-y^'+20y=0	y^{\prime\:\prime\:}-y^{\prime\:}+20y=0
limit as x approaches 3+of 5/(x-3)	\lim\:_{x\to\:3+}(\frac{5}{x-3})
tangent of (x-2)^6	tangent\:(x-2)^{6}
limit as x approaches 1 of 3x-2	\lim\:_{x\to\:1}(3x-2)
integral of ((sin(x))^3)/(1+(cos(x))^3)	\int\:\frac{(\sin(x))^{3}}{1+(\cos(x))^{3}}dx
derivative of 5/(5-x)	\frac{d}{dx}(\frac{5}{5-x})
integral of e^ysin(x)	\int\:e^{y}\sin(x)dx
slope of (3,1),(1,-8)	slope\:(3,1),(1,-8)
derivative of-sqrt(1-x^2)	derivative\:-\sqrt{1-x^{2}}
limit as t approaches 1 of sin(-pit)	\lim\:_{t\to\:1}(\sin(-πt))
derivative of e^{3x+2x^2}	\frac{d}{dx}(e^{3x+2x^{2}})
limit as h approaches 0 of h^2-3	\lim\:_{h\to\:0}(h^{2}-3)
d/(dt)(1/2 t^2)	\frac{d}{dt}(\frac{1}{2}t^{2})
25y^{''}+60y^'+36y=0	25y^{\prime\:\prime\:}+60y^{\prime\:}+36y=0
derivative of y=(x^2+7x-2)/(x-2)	derivative\:y=\frac{x^{2}+7x-2}{x-2}
(dx)/(dt)=4(x^2+1),x(pi/4)=1	\frac{dx}{dt}=4(x^{2}+1),x(\frac{π}{4})=1
integral of tan^4(2x)	\int\:\tan^{4}(2x)dx
t^5y^4-t^3y^'+6y=0	t^{5}y^{4}-t^{3}y^{\prime\:}+6y=0
y^'=(3(e^x+1))/(2y)	y^{\prime\:}=\frac{3(e^{x}+1)}{2y}
simplify d/(dd)((ax+b)/(cx+d))	simplify\:\frac{d}{dd}(\frac{ax+b}{cx+d})
derivative of-1/2 x^4cos(x)	\frac{d}{dx}(-\frac{1}{2}x^{4}\cos(x))
derivative of \sqrt[3]{x}ln(x)	\frac{d}{dx}(\sqrt[3]{x}\ln(x))
integral of 2/X	\int\:\frac{2}{X}dX
f(x)=5e^{5x}	f(x)=5e^{5x}
integral of (x^3)/(x^3-1)	\int\:\frac{x^{3}}{x^{3}-1}dx
f(x)=(\sqrt[3]{x^2-9})/x	f(x)=\frac{\sqrt[3]{x^{2}-9}}{x}
integral of 2xy^2+3x^2	\int\:2xy^{2}+3x^{2}dx
(\partial)/(\partial y)(y^2sin(x/y))	\frac{\partial\:}{\partial\:y}(y^{2}\sin(\frac{x}{y}))
area y=x^3,y=x^2-2x,[-1,1]	area\:y=x^{3},y=x^{2}-2x,[-1,1]
derivative of 2/3 x^3+x^2-12x+12	derivative\:\frac{2}{3}x^{3}+x^{2}-12x+12
laplacetransform f(t)=t	laplacetransform\:f(t)=t

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