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Popular Calculus Problems

integral from 1 to 2 of 3/(t^4)	\int\:_{1}^{2}\frac{3}{t^{4}}dt
x^2y^'+2x^3y=y^2(1+2x^2)	x^{2}y^{\prime\:}+2x^{3}y=y^{2}(1+2x^{2})
integral of sin(10x)cos(3x)	\int\:\sin(10x)\cos(3x)dx
derivative of 9sqrt(x)+2	\frac{d}{dx}(9\sqrt{x}+2)
integral of (x+2sqrt(x-1))/(2xsqrt(x-1))	\int\:\frac{x+2\sqrt{x-1}}{2x\sqrt{x-1}}dx
derivative of ((x^3-3))/((x^2+x-1))	derivative\:\frac{(x^{3}-3)}{(x^{2}+x-1)}
(2+x^2)y^'-2xy=0	(2+x^{2})y^{\prime\:}-2xy=0
slope of y=8x-x^2	slope\:y=8x-x^{2}
derivative of x^2-3xy+y^2	\frac{d}{dx}(x^{2}-3xy+y^{2})
derivative of ((sqrt(x)-2)/(sqrt(x)+2))	\frac{d}{dx}(\frac{(\sqrt{x}-2)}{\sqrt{x}+2})
y^{''}+30y=0	y^{\prime\:\prime\:}+30y=0
integral of (2x)/(2x-1)	\int\:\frac{2x}{2x-1}dx
integral of (2x^3-x+0)^3*(6x^2-1)	\int\:(2x^{3}-x+0)^{3}\cdot\:(6x^{2}-1)dx
derivative of 6^{sqrt(x)}	\frac{d}{dx}(6^{\sqrt{x}})
integral of xe^{-0.5x^2}	\int\:xe^{-0.5x^{2}}dx
integral from 0 to 2pi of sin^2(1/3 x)	\int\:_{0}^{2π}\sin^{2}(\frac{1}{3}x)dx
limit as x approaches 0 of (1+x)^{1/x}	\lim\:_{x\to\:0}((1+x)^{\frac{1}{x}})
derivative of ((x-1^2)/(x^2+2))	\frac{d}{dx}(\frac{(x-1)^{2}}{x^{2}+2})
derivative of f(x)=(x-1)(x^2-8x+7)	derivative\:f(x)=(x-1)(x^{2}-8x+7)
derivative of f(x)=(-cos(x))/(4x^2+2x-3)	derivative\:f(x)=\frac{-\cos(x)}{4x^{2}+2x-3}
inverse oflaplace 1/((s-5)^3)	inverselaplace\:\frac{1}{(s-5)^{3}}
(\partial)/(\partial x)(56e^{8x}y)	\frac{\partial\:}{\partial\:x}(56e^{8x}y)
integral from 0 to pi/2 of (sin(2x))	\int\:_{0}^{\frac{π}{2}}(\sin(2x))dx
limit as x approaches 1-of 2x^3+5x	\lim\:_{x\to\:1-}(2x^{3}+5x)
integral from-2 to 5 of (-2)	\int\:_{-2}^{5}(-2)dx
derivative of f(x)=x^2+5x-3	derivative\:f(x)=x^{2}+5x-3
limit as x approaches 7 of f(x)	\lim\:_{x\to\:7}(f(x))
(dy)/(dx)=((x-4))/((y-6))	\frac{dy}{dx}=\frac{(x-4)}{(y-6)}
(\partial)/(\partial x)(xye^{(-5y)})	\frac{\partial\:}{\partial\:x}(xye^{(-5y)})
integral of (cos(x))/(sin(x)-cos(x))	\int\:\frac{\cos(x)}{\sin(x)-\cos(x)}dx
integral of 1/(2x)	\int\:\frac{1}{2x}dx
integral from 1 to 4 of 1/((x-2)^{1/3)}	\int\:_{1}^{4}\frac{1}{(x-2)^{\frac{1}{3}}}dx
derivative of 10^{-x}	\frac{d}{dx}(10^{-x})
integral of x(8-x)^2	\int\:x(8-x)^{2}dx
y^'+sin(x)y=sin(x)	y^{\prime\:}+\sin(x)y=\sin(x)
limit as x approaches 2-of x^2+a	\lim\:_{x\to\:2-}(x^{2}+a)
tangent of f(x)= x/(x-3),\at x=0	tangent\:f(x)=\frac{x}{x-3},\at\:x=0
derivative of (sin(x))^3	derivative\:(\sin(x))^{3}
f(x)=-4x	f(x)=-4x
integral of (-sin(x))	\int\:(-\sin(x))dx
derivative of ln((x+1/x))	\frac{d}{dx}(\ln(\frac{x+1}{x}))
integral from 0 to 6 of 6x-x^2	\int\:_{0}^{6}6x-x^{2}dx
integral of y^2-4	\int\:y^{2}-4dy
integral of cos(x)sin^4(x)	\int\:\cos(x)\sin^{4}(x)dx
tangent of f(x)= 7/2 x^2-5x+1	tangent\:f(x)=\frac{7}{2}x^{2}-5x+1
limit as θ approaches 0 of θcot(5θ)	\lim\:_{θ\to\:0}(θ\cot(5θ))
derivative of (x^2-9/(x^2+9))	\frac{d}{dx}(\frac{x^{2}-9}{x^{2}+9})
x^{''}+x^'+2x=0	x^{\prime\:\prime\:}+x^{\prime\:}+2x=0
(dy)/(dx)=2y(3-y)	\frac{dy}{dx}=2y(3-y)
derivative of y=5arctan(x-sqrt(1+x^2))	derivative\:y=5\arctan(x-\sqrt{1+x^{2}})
integral of 1/(y^2-3y)	\int\:\frac{1}{y^{2}-3y}dy
area y=-x+4,y=(x^2)/3	area\:y=-x+4,y=\frac{x^{2}}{3}
derivative of csc^2(x-4)	\frac{d}{dx}(\csc^{2}(x)-4)
derivative of 4/(x^2+sqrt(x))	derivative\:\frac{4}{x^{2}+\sqrt{x}}
taylor e^{-x},0	taylor\:e^{-x},0
derivative of (2x+5(3x^2-4x+1))	\frac{d}{dx}((2x+5)(3x^{2}-4x+1))
maclaurin (x+1)(ln(x+1))	maclaurin\:(x+1)(\ln(x+1))
area e^{2x},e^{5x},x=1	area\:e^{2x},e^{5x},x=1
(\partial)/(\partial x)(xsqrt(1+y^9))	\frac{\partial\:}{\partial\:x}(x\sqrt{1+y^{9}})
(\partial)/(\partial x)(5e^{-x}cos(y))	\frac{\partial\:}{\partial\:x}(5e^{-x}\cos(y))
derivative of 1/(sqrt(1+4x^2+9x^4))	\frac{d}{dx}(\frac{1}{\sqrt{1+4x^{2}+9x^{4}}})
d/(dθ)(2-2sin(θ))	\frac{d}{dθ}(2-2\sin(θ))
derivative of cos(3\sqrt[5]{x^2})	\frac{d}{dx}(\cos(3\sqrt[5]{x^{2}}))
integral of (cos(ax+b))	\int\:(\cos(ax+b))dx
integral of (e^{2t})/(e^{2t)-1}	\int\:\frac{e^{2t}}{e^{2t}-1}dt
derivative of ln((1+tan(x)/(1+sin(x))))	\frac{d}{dx}(\ln(\frac{1+\tan(x)}{1+\sin(x)}))
integral of t/((t^2+1)^{19/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{19}{2}}}dt
f(x)=x^3sin(x)	f(x)=x^{3}\sin(x)
limit as x approaches infinity of xb	\lim\:_{x\to\:\infty\:}(xb)
integral of (3x^3)/(sqrt(7-9x^4))	\int\:\frac{3x^{3}}{\sqrt{7-9x^{4}}}dx
integral of 1/(xsqrt(4x-1))	\int\:\frac{1}{x\sqrt{4x-1}}dx
integral of (4x-1)/(\sqrt[3]{3x+1)}	\int\:\frac{4x-1}{\sqrt[3]{3x+1}}dx
integral of (x+1)e^{6x^2+12x}	\int\:(x+1)e^{6x^{2}+12x}dx
sqrt((1-cos(2x))/(1+sin(y)))+y^'=0	\sqrt{\frac{1-\cos(2x)}{1+\sin(y)}}+y^{\prime\:}=0
derivative of tan(xy)	\frac{d}{dx}(\tan(xy))
(\partial)/(\partial t)(t-2s)	\frac{\partial\:}{\partial\:t}(t-2s)
integral of 3z^3e^z	\int\:3z^{3}e^{z}dz
18xy^'-2y=-(x^2)/(y^{17)}	18xy^{\prime\:}-2y=-\frac{x^{2}}{y^{17}}
limit as x approaches 0 of (4^x-11^x)/x	\lim\:_{x\to\:0}(\frac{4^{x}-11^{x}}{x})
derivative of sqrt(10t^2-t)	derivative\:\sqrt{10t^{2}-t}
derivative of y=2ln(x)	derivative\:y=2\ln(x)
integral of (x^2)/((1-x^2)^2)	\int\:\frac{x^{2}}{(1-x^{2})^{2}}dx
derivative of 2/(x^2-3/(x^{1/3)})	\frac{d}{dx}(\frac{2}{x^{2}}-\frac{3}{x^{\frac{1}{3}}})
derivative of 7x-4sqrt(x)	\frac{d}{dx}(7x-4\sqrt{x})
f(t)=cos(t)	f(t)=\cos(t)
limit as x approaches 0 of 2xcos(1/x)-2	\lim\:_{x\to\:0}(2x\cos(\frac{1}{x})-2)
derivative of f(x)=(4x+2)^{-1}	derivative\:f(x)=(4x+2)^{-1}
integral of (1/(sqrt(9+x^2)))	\int\:(\frac{1}{\sqrt{9+x^{2}}})dx
integral of 1/(sec(y)tan(y))	\int\:\frac{1}{\sec(y)\tan(y)}dy
y^'+2y=e^{3x}	y^{\prime\:}+2y=e^{3x}
derivative of 5tan(2x^3)	\frac{d}{dx}(5\tan(2x^{3}))
integral of sqrt(bx)	\int\:\sqrt{bx}dx
sum from n=1 to infinity of 9(1/10)^n	\sum\:_{n=1}^{\infty\:}9(\frac{1}{10})^{n}
derivative of x^{cos(x})	\frac{d}{dx}(x^{\cos(x)})
(\partial)/(\partial x)(sin(-3x)cos(6y))	\frac{\partial\:}{\partial\:x}(\sin(-3x)\cos(6y))
derivative of (cos(x)^5)	\frac{d}{dx}((\cos(x))^{5})
limit as x approaches 0 of arcsin(x)	\lim\:_{x\to\:0}(\arcsin(x))
derivative of log_{2}(x^2-9x)	\frac{d}{dx}(\log_{2}(x^{2}-9x))
derivative of (x^2-1(x^2-4)(x^2-9))	\frac{d}{dx}((x^{2}-1)(x^{2}-4)(x^{2}-9))
(\partial)/(\partial x)(50-(4x^2+y^2))	\frac{\partial\:}{\partial\:x}(50-(4x^{2}+y^{2}))

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