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Popular Calculus Problems

sum from n=1 to infinity of-3/(2^n)	\sum\:_{n=1}^{\infty\:}-\frac{3}{2^{n}}
integral of (x^2)/(sqrt(13-4x+x^2))	\int\:\frac{x^{2}}{\sqrt{13-4x+x^{2}}}dx
derivative of (-3x-sqrt(16x))/(2x^{1/3)}	derivative\:\frac{-3x-\sqrt{16x}}{2x^{\frac{1}{3}}}
y^{''}+20y^'+200y=0	y^{\prime\:\prime\:}+20y^{\prime\:}+200y=0
y^{''}+8y^'+13y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+13y=0
x(dy)/(dx)-y=x^2y^2	x\frac{dy}{dx}-y=x^{2}y^{2}
taylor 1/((x^2+25)^{-3)}	taylor\:\frac{1}{(x^{2}+25)^{-3}}
y^'+20y=24	y^{\prime\:}+20y=24
derivative of f(x)=(x^5-2x)^2	derivative\:f(x)=(x^{5}-2x)^{2}
integral of x^2-9	\int\:x^{2}-9dx
limit as x approaches 0 of (x^2-5x)/x	\lim\:_{x\to\:0}(\frac{x^{2}-5x}{x})
integral of 24sin(x)	\int\:24\sin(x)dx
integral of (6x+3)/(x^2+11x+28)	\int\:\frac{6x+3}{x^{2}+11x+28}dx
sum from n=2 to infinity of 1/(4^{2n)}	\sum\:_{n=2}^{\infty\:}\frac{1}{4^{2n}}
integral of 1/(4x^2+12x+18)	\int\:\frac{1}{4x^{2}+12x+18}dx
(\partial)/(\partial x)(4+x^3+y^3-3xy)	\frac{\partial\:}{\partial\:x}(4+x^{3}+y^{3}-3xy)
laplacetransform 2e^{-t}-3/2 e^{-2t}	laplacetransform\:2e^{-t}-\frac{3}{2}e^{-2t}
derivative of sec(x-2cos(x))	\frac{d}{dx}(\sec(x)-2\cos(x))
integral of 8sin(t)	\int\:8\sin(t)dt
(\partial)/(\partial x)(3x^4y^5)	\frac{\partial\:}{\partial\:x}(3x^{4}y^{5})
derivative of (x^2+1^5)	\frac{d}{dx}((x^{2}+1)^{5})
integral of sqrt(cos(x)-cos^3(x))	\int\:\sqrt{\cos(x)-\cos^{3}(x)}dx
derivative of f(x)=7+x^2	derivative\:f(x)=7+x^{2}
derivative of 7e^{7e^x+x}	derivative\:7e^{7e^{x}+x}
extreme f(z)=3x+2z+4xz	extreme\:f(z)=3x+2z+4xz
derivative of f(x)=12x^4+3x^3+5x^{-2}-4	derivative\:f(x)=12x^{4}+3x^{3}+5x^{-2}-4
integral of sin^2(bx)cos(bx)	\int\:\sin^{2}(bx)\cos(bx)dx
integral of sqrt(3x-2)	\int\:\sqrt{3x-2}dx
derivative of 5/(x+2)	\frac{d}{dx}(\frac{5}{x+2})
area x^2-1,-x+2,[0,1]	area\:x^{2}-1,-x+2,[0,1]
integral of (sin(4e^{-3x}))/(e^{3x)}	\int\:\frac{\sin(4e^{-3x})}{e^{3x}}dx
integral of (sec^2(θ))/(sqrt(1+2tan(θ)))	\int\:\frac{\sec^{2}(θ)}{\sqrt{1+2\tan(θ)}}dθ
tangent of f(x)=x^4,\at x=6.87	tangent\:f(x)=x^{4},\at\:x=6.87
integral of x^3+2x+1	\int\:x^{3}+2x+1dx
derivative of f(x)=(2x^2)/(x+3)	derivative\:f(x)=\frac{2x^{2}}{x+3}
derivative of (2x-1)^2	derivative\:(2x-1)^{2}
limit as x approaches 0-of 18-x^2	\lim\:_{x\to\:0-}(18-x^{2})
derivative of 1/(x+c)	\frac{d}{dx}(\frac{1}{x+c})
integral of (2x+1)^9	\int\:(2x+1)^{9}dx
d/(dt)(t^2+2)	\frac{d}{dt}(t^{2}+2)
integral of 3xe^{3x}	\int\:3xe^{3x}dx
derivative of f(x)=(cos(t))/(t^7)	derivative\:f(x)=\frac{\cos(t)}{t^{7}}
x^{''}-3x^'=e^{-3t}	x^{\prime\:\prime\:}-3x^{\prime\:}=e^{-3t}
integral from-infinity to 0 of 1/(3-4x)	\int\:_{-\infty\:}^{0}\frac{1}{3-4x}dx
integral from 0 to pi/(10) of tan(5x)	\int\:_{0}^{\frac{π}{10}}\tan(5x)dx
integral of (5-10x^2)/(4x^3-6x+15)	\int\:\frac{5-10x^{2}}{4x^{3}-6x+15}dx
limit as x approaches 2 of \sqrt[3]{x^2+12}	\lim\:_{x\to\:2}(\sqrt[3]{x^{2}+12})
area-x^2-x+9,-0.75x+6,x=0	area\:-x^{2}-x+9,-0.75x+6,x=0
(\partial)/(\partial x)(x^2y^3z)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}z)
integral of 1/(x+xln(x))	\int\:\frac{1}{x+x\ln(x)}dx
t^2y^{''}-3ty^'+4y=t^{5/2}	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}+4y=t^{\frac{5}{2}}
(\partial)/(\partial y)(xcos(yz))	\frac{\partial\:}{\partial\:y}(x\cos(yz))
derivative of (200/x)	\frac{d}{dx}(\frac{200}{x})
integral from 0 to 0.5 of 100x	\int\:_{0}^{0.5}100xdx
integral of ((x+9))/(x^2+4)	\int\:\frac{(x+9)}{x^{2}+4}dx
implicit (dy)/(dx),xy=2	implicit\:\frac{dy}{dx},xy=2
(\partial)/(\partial y)(e^{2x+5y})	\frac{\partial\:}{\partial\:y}(e^{2x+5y})
integral from-1 to 2 of x-6x^2	\int\:_{-1}^{2}x-6x^{2}dx
integral of (15-15x)/(1-sqrt(x))	\int\:\frac{15-15x}{1-\sqrt{x}}dx
integral of y^2sin(8y)	\int\:y^{2}\sin(8y)dy
derivative of (x^2^{1/3})	\frac{d}{dx}((x^{2})^{\frac{1}{3}})
limit as x approaches 0-of (e^{-x})/(x(x+2)^2)	\lim\:_{x\to\:0-}(\frac{e^{-x}}{x(x+2)^{2}})
(sqrt(x)+x)(dy)/(dx)=sqrt(y)+y	(\sqrt{x}+x)\frac{dy}{dx}=\sqrt{y}+y
integral of x^2(1+2x^3)^2	\int\:x^{2}(1+2x^{3})^{2}dx
tangent of f(x)=6sec(x),\at x= pi/3	tangent\:f(x)=6\sec(x),\at\:x=\frac{π}{3}
derivative of (x^2^5)	\frac{d}{dx}((x^{2})^{5})
integral of (16^x+20^x)/(4^x)	\int\:\frac{16^{x}+20^{x}}{4^{x}}dx
xy^'+3y-3=0	xy^{\prime\:}+3y-3=0
integral of (ln(x))/x-((ln(x))^2)/x	\int\:\frac{\ln(x)}{x}-\frac{(\ln(x))^{2}}{x}dx
integral from 0 to pi of (4e^x+7sin(x))	\int\:_{0}^{π}(4e^{x}+7\sin(x))dx
integral of (23)/(x^3-27)	\int\:\frac{23}{x^{3}-27}dx
derivative of arctan((2x/(1-x^2)))	\frac{d}{dx}(\arctan(\frac{2x}{1-x^{2}}))
limit as x approaches 0 of (e^x-1)/(16x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{16x})
derivative of x^4-8x^2+1	\frac{d}{dx}(x^{4}-8x^{2}+1)
integral of arcsin(y)	\int\:\arcsin(y)dy
integral from-infinity to 0 of 1/(1+x^2)	\int\:_{-\infty\:}^{0}\frac{1}{1+x^{2}}dx
derivative of ln(5x+1)	\frac{d}{dx}(\ln(5x+1))
derivative of f(x)=(19)/(sqrt(x^5))	derivative\:f(x)=\frac{19}{\sqrt{x^{5}}}
derivative of-2log_{6}(x)	\frac{d}{dx}(-2\log_{6}(x))
derivative of e^{9x}	derivative\:e^{9x}
implicit (dy)/(dx),sqrt(xy)=9+x^2y	implicit\:\frac{dy}{dx},\sqrt{xy}=9+x^{2}y
derivative of ln(x/(x+2))	\frac{d}{dx}(\ln(\frac{x}{x+2}))
integral of x(3+2x)^{10}	\int\:x(3+2x)^{10}dx
derivative of sin(x-e^{-x})	\frac{d}{dx}(\sin(x)-e^{-x})
integral of θcos(pi)θ	\int\:θ\cos(π)θdθ
limit as x approaches 0 of xln(2x)	\lim\:_{x\to\:0}(x\ln(2x))
integral of (11x^3)/(sqrt(1+x^2))	\int\:\frac{11x^{3}}{\sqrt{1+x^{2}}}dx
integral of (2r+1)/(r^2-3r+2)	\int\:\frac{2r+1}{r^{2}-3r+2}dr
integral of-3\|x\|	\int\:-3\left\|x\right\|dx
limit as x approaches infinity of ((e^{x^5}))/(5-x^6)	\lim\:_{x\to\:\infty\:}(\frac{(e^{x^{5}})}{5-x^{6}})
derivative of sin(cos(3x))	\frac{d}{dx}(\sin(\cos(3x)))
integral of (sqrt(x+1)+1)/(sqrt(x+1)-1)	\int\:\frac{\sqrt{x+1}+1}{\sqrt{x+1}-1}dx
integral of (x^2+1)ln(x)	\int\:(x^{2}+1)\ln(x)dx
integral of (-x)/(1-x)	\int\:\frac{-x}{1-x}dx
integral of sec^4(x	\int\:\sec^{4}(d)xdx
(dh)/(dt)=4-16t^2	\frac{dh}{dt}=4-16t^{2}
derivative of g(x)=x^2+3x^3	derivative\:g(x)=x^{2}+3x^{3}
(dy)/(dx)(xy)=7	\frac{dy}{dx}(xy)=7
derivative of f(x)=(x^2-7)/(16-x^2)	derivative\:f(x)=\frac{x^{2}-7}{16-x^{2}}
integral of log_{a}(x)	\int\:\log_{a}(x)dx

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