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Popular Calculus Problems

integral from 0 to 1/3 of arcsin(3y)	\int\:_{0}^{\frac{1}{3}}\arcsin(3y)dy
limit as x approaches pi of (3x+1)/(1-x)	\lim\:_{x\to\:π}(\frac{3x+1}{1-x})
derivative of (ln(3x)^2)	\frac{d}{dx}((\ln(3x))^{2})
area x^3,x^2+x,-1,2	area\:x^{3},x^{2}+x,-1,2
derivative of (80sin(0.6x)/x+15)	\frac{d}{dx}(\frac{80\sin(0.6x)}{x}+15)
slope of (7,2),(8,y)	slope\:(7,2),(8,y)
sum from n=1 to infinity of 2(2/3)^n	\sum\:_{n=1}^{\infty\:}2(\frac{2}{3})^{n}
(\partial)/(\partial y)(xsin(2y))	\frac{\partial\:}{\partial\:y}(x\sin(2y))
tangent of y=3x^3-x^2+2,(2,22)	tangent\:y=3x^{3}-x^{2}+2,(2,22)
limit as x approaches-1 of (\|x\|-1)/(x+1)	\lim\:_{x\to\:-1}(\frac{\left\|x\right\|-1}{x+1})
limit as h approaches 0 of (7(a+h)^2-7a^2)/h	\lim\:_{h\to\:0}(\frac{7(a+h)^{2}-7a^{2}}{h})
derivative of f(x)=(x^2)/(x^2-1)	derivative\:f(x)=\frac{x^{2}}{x^{2}-1}
integral of 1/(sin(5x)cos(5x))	\int\:\frac{1}{\sin(5x)\cos(5x)}dx
integral of 8e^{-t}	\int\:8e^{-t}dt
derivative of-(x^2)/(20)+230x-74000	derivative\:-\frac{x^{2}}{20}+230x-74000
derivative of y=x^2+4	derivative\:y=x^{2}+4
y^{''}+16y=e^{3x}	y^{\prime\:\prime\:}+16y=e^{3x}
integral of (-sin(8t))/8	\int\:\frac{-\sin(8t)}{8}dt
derivative of 7cos(x+7xsin(x))	\frac{d}{dx}(7\cos(x)+7x\sin(x))
integral of (16)/(sqrt(49-36x^2))	\int\:\frac{16}{\sqrt{49-36x^{2}}}dx
d/(ds)(s/t)	\frac{d}{ds}(\frac{s}{t})
integral of 3/(6x-x^2)	\int\:\frac{3}{6x-x^{2}}dx
derivative of x^3cos(x-9xsin(x)-9cos(x))	\frac{d}{dx}(x^{3}\cos(x)-9x\sin(x)-9\cos(x))
limit as x approaches 0 of 0/(x^4)	\lim\:_{x\to\:0}(\frac{0}{x^{4}})
derivative of-3x^{3/2}-1	derivative\:-3x^{\frac{3}{2}}-1
derivative of f(x)= 9/x	derivative\:f(x)=\frac{9}{x}
derivative of sqrt(1/x+x)-sqrt(1/x-x)	\frac{d}{dx}(\sqrt{\frac{1}{x}+x}-\sqrt{\frac{1}{x}-x})
y^'=t-y	y^{\prime\:}=t-y
area xcos(x),-pi/2 , pi/2	area\:x\cos(x),-\frac{π}{2},\frac{π}{2}
(\partial)/(\partial x)(-cos(x)+xcos(y))	\frac{\partial\:}{\partial\:x}(-\cos(x)+x\cos(y))
derivative of xcos(xcos(y))	\frac{d}{dx}(x\cos(x)\cos(y))
integral of e^{x/2}	\int\:e^{\frac{x}{2}}dx
derivative of 7x^{-12}	\frac{d}{dx}(7x^{-12})
derivative of 4x^2+2x	\frac{d}{dx}(4x^{2}+2x)
integral of log_{10}(x)	\int\:\log_{10}(x)dx
derivative of arcsec(5x^4)	\frac{d}{dx}(\arcsec(5x^{4}))
(\partial)/(\partial y)(e^{3x}sin(2y))	\frac{\partial\:}{\partial\:y}(e^{3x}\sin(2y))
derivative of cos(3y)	derivative\:\cos(3y)
derivative of e^{-5x^4}	\frac{d}{dx}(e^{-5x^{4}})
integral of (x^2+3)sin(x)	\int\:(x^{2}+3)\sin(x)dx
y=3(1)^2-5(1)+9	y=3(1)^{2}-5(1)+9
integral of (cos(x))/(sin^4(x)-16)	\int\:\frac{\cos(x)}{\sin^{4}(x)-16}dx
integral of (2x^2-4)/(x^2(x-2))	\int\:\frac{2x^{2}-4}{x^{2}(x-2)}dx
derivative of y=sqrt(x)(x-14)	derivative\:y=\sqrt{x}(x-14)
integral from 2y^2+2z^2 to 2 of x	\int\:_{2y^{2}+2z^{2}}^{2}xdx
1/(1-x^2)(dy)/(dx)+1/(1-x)y=e^{-1/2 x^2}	\frac{1}{1-x^{2}}\frac{dy}{dx}+\frac{1}{1-x}y=e^{-\frac{1}{2}x^{2}}
integral of sqrt(x)(2+xsqrt(x))^5	\int\:\sqrt{x}(2+x\sqrt{x})^{5}dx
derivative of-e^{-x}x^2+e^{-x}x	\frac{d}{dx}(-e^{-x}x^{2}+e^{-x}x)
taylor e^{-x},5	taylor\:e^{-x},5
(dy)/(dx)=sqrt(xy)	\frac{dy}{dx}=\sqrt{xy}
derivative of h(x)= 1/((-x^2+x-2)^5)	derivative\:h(x)=\frac{1}{(-x^{2}+x-2)^{5}}
(\partial)/(\partial x)((x^2+2y)/(x^3-y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+2y}{x^{3}-y^{2}})
derivative of ln(xsqrt(x^2-5))	\frac{d}{dx}(\ln(x\sqrt{x^{2}-5}))
sum from n=0 to infinity of (x^n)/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{4^{n}}
tangent of 2x^2,\at 2	tangent\:2x^{2},\at\:2
derivative of xe^{2x-y^2}	\frac{d}{dx}(xe^{2x-y^{2}})
(dy)/(dx)-y=x	\frac{dy}{dx}-y=x
(\partial)/(\partial x)(x^2y+2x+y)	\frac{\partial\:}{\partial\:x}(x^{2}y+2x+y)
tangent of f(x)=6cos(x),\at x= pi/3	tangent\:f(x)=6\cos(x),\at\:x=\frac{π}{3}
integral of 1/(xln^5(x))	\int\:\frac{1}{x\ln^{5}(x)}dx
limit as x approaches 3 of 1/(x+2)	\lim\:_{x\to\:3}(\frac{1}{x+2})
limit as x approaches 0-of 2+3e^{-3/x}	\lim\:_{x\to\:0-}(2+3e^{-\frac{3}{x}})
derivative of-5sin(x)	derivative\:of-5\sin(x)
limit as x approaches-3 of (2-x)/(3-x)	\lim\:_{x\to\:-3}(\frac{2-x}{3-x})
(\partial)/(\partial x)(2x(2+y)^{-1})	\frac{\partial\:}{\partial\:x}(2x(2+y)^{-1})
sum from n=1 to infinity of 9-6/(n^2)	\sum\:_{n=1}^{\infty\:}9-\frac{6}{n^{2}}
limit as x approaches 1 of-x^2+1	\lim\:_{x\to\:1}(-x^{2}+1)
integral of 7e^{8x}	\int\:7e^{8x}dx
sum from n=0 to infinity of ln^n(3)	\sum\:_{n=0}^{\infty\:}\ln^{n}(3)
ty^'+(t+1)y=t,y(ln(5))=1	ty^{\prime\:}+(t+1)y=t,y(\ln(5))=1
derivative of (e^{3x^2})/(5x)	derivative\:\frac{e^{3x^{2}}}{5x}
derivative of 6(1-x/(12)^2)	\frac{d}{dx}(6(1-\frac{x}{12})^{2})
laplacetransform y^2	laplacetransform\:y^{2}
limit as t approaches 0 of (4t+2)/(t+1)	\lim\:_{t\to\:0}(\frac{4t+2}{t+1})
slope of (19.3)(20.3)	slope\:(19.3)(20.3)
derivative of xe^{-x+1}	derivative\:xe^{-x+1}
integral of 0.5^x	\int\:0.5^{x}dx
derivative of x^2+y^2-1	\frac{d}{dx}(x^{2}+y^{2}-1)
derivative of sqrt(e^{sin(x)})	\frac{d}{dx}(\sqrt{e^{\sin(x)}})
limit as x approaches 2 of (x-2)/((x-2))	\lim\:_{x\to\:2}(\frac{x-2}{(x-2)})
tangent of y=x+sin(x)	tangent\:y=x+\sin(x)
derivative of (2x^3-12x^{4/3})	\frac{d}{dx}((2x^{3}-12x)^{\frac{4}{3}})
(\partial)/(\partial x)(x/(x^2+4y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+4y^{2}})
integral of 1/((x^2-x))	\int\:\frac{1}{(x^{2}-x)}dx
(\partial)/(\partial x)(ycos(x-y))	\frac{\partial\:}{\partial\:x}(y\cos(x-y))
64y^{''}+80y^'+25y=0,y(0)=a,y^'(0)=-5	64y^{\prime\:\prime\:}+80y^{\prime\:}+25y=0,y(0)=a,y^{\prime\:}(0)=-5
tangent of f(x)=ln(x^2-9x+1),\at x=9	tangent\:f(x)=\ln(x^{2}-9x+1),\at\:x=9
integral of e^{-x-y}	\int\:e^{-x-y}dx
integral of 7arcsin(x)	\int\:7\arcsin(x)dx
derivative of ((x^2+3/(x^2-3))^5)	\frac{d}{dx}((\frac{x^{2}+3}{x^{2}-3})^{5})
integral of cos^{18}(x)sin(x)	\int\:\cos^{18}(x)\sin(x)dx
derivative of-5(7x^2+4)^{-6}	derivative\:-5(7x^{2}+4)^{-6}
limit as z approaches 10 of 1/(z-10)	\lim\:_{z\to\:10}(\frac{1}{z-10})
integral of arccos(1/x)	\int\:\arccos(\frac{1}{x})dx
area y=8x^2-2x,y=x^3-8x+3	area\:y=8x^{2}-2x,y=x^{3}-8x+3
(dy)/(dx)=(y^2+xy+x^2)/(x^2)	\frac{dy}{dx}=\frac{y^{2}+xy+x^{2}}{x^{2}}
integral of sin^2(y)cos(y)	\int\:\sin^{2}(y)\cos(y)dy
inverse oflaplace 1/((s-1)(s+4))	inverselaplace\:\frac{1}{(s-1)(s+4)}
integral of (4x^3-2x)(x^4-x^2-5)^3	\int\:(4x^{3}-2x)(x^{4}-x^{2}-5)^{3}dx
limit as x approaches+0+of arctan(2/x)	\lim\:_{x\to\:+0+}(\arctan(\frac{2}{x}))

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