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Popular Calculus Problems

integral from-1 to 2 of (8-x^2)	\int\:_{-1}^{2}(8-x^{2})dx
(\partial)/(\partial x)((5x+9y)^{10})	\frac{\partial\:}{\partial\:x}((5x+9y)^{10})
derivative of 3cos(4x)	\frac{d}{dx}(3\cos(4x))
(\partial)/(\partial t)(4e^{sin(x+3ct)})	\frac{\partial\:}{\partial\:t}(4e^{\sin(x+3ct)})
integral from 0 to 4 of pi(sqrt(x-1))^2	\int\:_{0}^{4}π(\sqrt{x-1})^{2}dx
limit as x approaches-5 of 2/((x+5)^4)	\lim\:_{x\to\:-5}(\frac{2}{(x+5)^{4}})
integral of 1024sin^4(x)cos^4(x)	\int\:1024\sin^{4}(x)\cos^{4}(x)dx
integral of (t^5)/((t^3+1)^2)	\int\:\frac{t^{5}}{(t^{3}+1)^{2}}dt
derivative of (x^n-1/(x-1))	\frac{d}{dx}(\frac{x^{n}-1}{x-1})
derivative of y=xsqrt(3600-x^2)	derivative\:y=x\sqrt{3600-x^{2}}
derivative of 2t^3cos(t)	derivative\:2t^{3}\cos(t)
(\partial)/(\partial z)(e^{xyz^2+z})	\frac{\partial\:}{\partial\:z}(e^{xyz^{2}+z})
integral from 0 to pi/4 of sin^5(2x)	\int\:_{0}^{\frac{π}{4}}\sin^{5}(2x)dx
(\partial)/(\partial x)(4x^2+4y^3)	\frac{\partial\:}{\partial\:x}(4x^{2}+4y^{3})
limit as x approaches infinity of (((a^{(1/x)}+b^{(1/x)})^x))/(2^x)	\lim\:_{x\to\:\infty\:}(\frac{((a^{(\frac{1}{x})}+b^{(\frac{1}{x})})^{x})}{2^{x}})
y^'+10(tan(10x))y=9cos(10x)	y^{\prime\:}+10(\tan(10x))y=9\cos(10x)
integral of (3x^2+4)sqrt(x-1)	\int\:(3x^{2}+4)\sqrt{x-1}dx
(dx)/(dt)=-1/2 x+t	\frac{dx}{dt}=-\frac{1}{2}x+t
d/(dt)(7sin^3(t))	\frac{d}{dt}(7\sin^{3}(t))
integral from 4 to 7 of (x-5)^2	\int\:_{4}^{7}(x-5)^{2}dx
y^'+y=e^x,y(0)=6	y^{\prime\:}+y=e^{x},y(0)=6
area y=6cos(3x),y=6sin(3x),(0, pi/8)	area\:y=6\cos(3x),y=6\sin(3x),(0,\frac{π}{8})
(\partial)/(\partial x)(x/(x^5-y^5))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{5}-y^{5}})
limit as x approaches 2 of (\|2-x\|)/(2-x)	\lim\:_{x\to\:2}(\frac{\left\|2-x\right\|}{2-x})
integral of sin(x)csc(x)	\int\:\sin(x)\csc(x)dx
f(x)=e^{2x^2}	f(x)=e^{2x^{2}}
inverse oflaplace 1/(s^2(s^2+4s+5))	inverselaplace\:\frac{1}{s^{2}(s^{2}+4s+5)}
integral of sin^2(3x)cos^3(3x)	\int\:\sin^{2}(3x)\cos^{3}(3x)dx
limit as x approaches 2 of 6-2x	\lim\:_{x\to\:2}(6-2x)
limit as x approaches 0 of 5-x^2	\lim\:_{x\to\:0}(5-x^{2})
(\partial)/(\partial x)(1-2x^2-x-4y^2+y)	\frac{\partial\:}{\partial\:x}(1-2x^{2}-x-4y^{2}+y)
integral from 0 to 1 of x/(sqrt(1+x))	\int\:_{0}^{1}\frac{x}{\sqrt{1+x}}dx
d/(dt)(e^{3t})	\frac{d}{dt}(e^{3t})
derivative of acos(t+bsin(t))	\frac{d}{dx}(a\cos(t)+b\sin(t))
area y=6x,y= 2/3 x,y=40-x^2	area\:y=6x,y=\frac{2}{3}x,y=40-x^{2}
integral of x(2x^2+1)^{3/2}	\int\:x(2x^{2}+1)^{\frac{3}{2}}dx
(\partial)/(\partial x)(x^2*cos(xy))	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:\cos(xy))
area y=10x^2,y^2= 1/10 x	area\:y=10x^{2},y^{2}=\frac{1}{10}x
limit as x approaches 3-of 1/((x-3)^2)	\lim\:_{x\to\:3-}(\frac{1}{(x-3)^{2}})
integral of 1/(2xsqrt(16x^2-8))	\int\:\frac{1}{2x\sqrt{16x^{2}-8}}dx
integral of 4^{3x}	\int\:4^{3x}dx
derivative of 6t^2+8	derivative\:6t^{2}+8
integral of (14)/(14+e^x)	\int\:\frac{14}{14+e^{x}}dx
f(t)=t^3-2t^2+5t+4	f(t)=t^{3}-2t^{2}+5t+4
tangent of f(x)=(e^{-x})/(x+1),\at x=1	tangent\:f(x)=\frac{e^{-x}}{x+1},\at\:x=1
derivative of x/((1-x))	\frac{d}{dx}(\frac{x}{(1-x)})
integral of x^3sqrt(x-4)	\int\:x^{3}\sqrt{x-4}dx
derivative of (2x^2-3x+1/(2x+1))	\frac{d}{dx}(\frac{2x^{2}-3x+1}{2x+1})
sum from n=1 to infinity of ln(1+2/n)	\sum\:_{n=1}^{\infty\:}\ln(1+\frac{2}{n})
derivative of 3x^{1/4}	\frac{d}{dx}(3x^{\frac{1}{4}})
derivative of 2x^3-3x^2-72x+3	\frac{d}{dx}(2x^{3}-3x^{2}-72x+3)
parity y=ln(sec(x)+tan(x))	parity\:y=\ln(\sec(x)+\tan(x))
derivative of (2x-45(x^2+162))	\frac{d}{dx}((2x-45)(x^{2}+162))
derivative of sin^3(cos^2(e^{x^2+1}))	\frac{d}{dx}(\sin^{3}(\cos^{2}(e^{x^{2}+1})))
integral of (3x-2)\sqrt[5]{x}	\int\:(3x-2)\sqrt[5]{x}dx
derivative of y=(2x)/(5-cot(x))	derivative\:y=\frac{2x}{5-\cot(x)}
(\partial)/(\partial y)(4x^2+3y^4)	\frac{\partial\:}{\partial\:y}(4x^{2}+3y^{4})
limit as x approaches 0 of (tan(x)-x)/x	\lim\:_{x\to\:0}(\frac{\tan(x)-x}{x})
integral of cot^2(3x)	\int\:\cot^{2}(3x)dx
integral of (1+sqrt(x))^3	\int\:(1+\sqrt{x})^{3}dx
integral from 0 to 5 of sqrt((5-x)/5)	\int\:_{0}^{5}\sqrt{\frac{5-x}{5}}dx
derivative of sqrt((x^3-1/(x^3+1)))	\frac{d}{dx}(\sqrt{\frac{x^{3}-1}{x^{3}+1}})
f(x)=(xcos(x)+pi)/(x-pi)	f(x)=\frac{x\cos(x)+π}{x-π}
integral of 6tan^3(2x)sec^5(2x)	\int\:6\tan^{3}(2x)\sec^{5}(2x)dx
integral of 1/(5+3x)	\int\:\frac{1}{5+3x}dx
derivative of 7e^x+8/(\sqrt[3]{x})	\frac{d}{dx}(7e^{x}+\frac{8}{\sqrt[3]{x}})
derivative of (1+3/x ^x)	\frac{d}{dx}((1+\frac{3}{x})^{x})
(\partial)/(\partial x)(((2x-5y))/(2x+5y))	\frac{\partial\:}{\partial\:x}(\frac{(2x-5y)}{2x+5y})
integral from 0 to pi of 6sin^4(x)	\int\:_{0}^{π}6\sin^{4}(x)dx
y=sqrt(r^2-x^2),y=0	y=\sqrt{r^{2}-x^{2}},y=0
(\partial)/(\partial x)((ln(x))^2)	\frac{\partial\:}{\partial\:x}((\ln(x))^{2})
tangent of sqrt(x),\at x=144	tangent\:\sqrt{x},\at\:x=144
integral of (x^3+x^2-x^5)/(x^6)	\int\:\frac{x^{3}+x^{2}-x^{5}}{x^{6}}dx
derivative of 1/4 (x^4+8)	\frac{d}{dx}(\frac{1}{4}(x^{4}+8))
derivative of g(x)=3x^4-140x^3	derivative\:g(x)=3x^{4}-140x^{3}
integral of 1/t	\int\:\frac{1}{t}dt
derivative of 4x^3y^{-2}	\frac{d}{dx}(4x^{3}y^{-2})
derivative of cos^n(x)	\frac{d}{dx}(\cos^{n}(x))
(\partial)/(\partial x)(-x)	\frac{\partial\:}{\partial\:x}(-x)
derivative of x/(e^x-100x)	\frac{d}{dx}(\frac{x}{e^{x}-100x})
derivative of sqrt(r)	derivative\:\sqrt{r}
derivative of-1/2 tan(x)	\frac{d}{dx}(-\frac{1}{2}\tan(x))
integral of (32)/(32+e^x)	\int\:\frac{32}{32+e^{x}}dx
taylor x^{3/2}	taylor\:x^{\frac{3}{2}}
limit as x approaches 7 of 2-sqrt(x-3)	\lim\:_{x\to\:7}(2-\sqrt{x-3})
integral of e^xsqrt(39+e^x)	\int\:e^{x}\sqrt{39+e^{x}}dx
tangent of f(x)=sqrt(x^3+3),(1,2)	tangent\:f(x)=\sqrt{x^{3}+3},(1,2)
integral of-3x	\int\:-3xdx
laplacetransform e^{3t}	laplacetransform\:e^{3t}
integral of 1/(sqrt(x^2+4x))	\int\:\frac{1}{\sqrt{x^{2}+4x}}dx
y^{''}-y^'-2y=-6t+6t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-6t+6t^{2}
integral of 1/(2x^3+x)	\int\:\frac{1}{2x^{3}+x}dx
(\partial)/(\partial x)((0.5x^2+0.5y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((0.5x^{2}+0.5y^{2})^{\frac{1}{2}})
integral from 0 to pi/2 of cos^5(1)	\int\:_{0}^{\frac{π}{2}}\cos^{5}(1)dx
y^{''}-4y^'+4y=t^{-6}e^{2t}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=t^{-6}e^{2t}
(\partial)/(\partial y)(xe^{x^2y})	\frac{\partial\:}{\partial\:y}(xe^{x^{2}y})
derivative of sin(sqrt(x-1))	\frac{d}{dx}(\sin(\sqrt{x-1}))
limit as x approaches 2 of sqrt(2x)	\lim\:_{x\to\:2}(\sqrt{2x})
y^{''}-4y^'+2y=0,y(0)=0,y^'(0)=5	y^{\prime\:\prime\:}-4y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=5
y^{''}-y=e^t	y^{\prime\:\prime\:}-y=e^{t}

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