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Popular Calculus Problems

taylor e^{x+2}	taylor\:e^{x+2}
(4+x)y^'=7y	(4+x)y^{\prime\:}=7y
limit as x approaches 0 of 3x^2+2x	\lim\:_{x\to\:0}(3x^{2}+2x)
integral of \sqrt[7]{x^2}	\int\:\sqrt[7]{x^{2}}dx
derivative of f(x)=(x^2+1)(x^3+1)	derivative\:f(x)=(x^{2}+1)(x^{3}+1)
(\partial)/(\partial z)(x+e^z+y)	\frac{\partial\:}{\partial\:z}(x+e^{z}+y)
xy^'+ln(x)y=0	xy^{\prime\:}+\ln(x)y=0
derivative of f(x)=2x^3+3x^2-12x+2	derivative\:f(x)=2x^{3}+3x^{2}-12x+2
limit as x approaches 4-of (x+5)/(x-4)	\lim\:_{x\to\:4-}(\frac{x+5}{x-4})
tangent of y=x^2+2x-1,(1,2)	tangent\:y=x^{2}+2x-1,(1,2)
area sqrt(x),y=2,x=0	area\:\sqrt{x},y=2,x=0
derivative of f(x)=(x^3)/(x-1)	derivative\:f(x)=\frac{x^{3}}{x-1}
sum from n=0 to infinity of (2/7)^{n/2}	\sum\:_{n=0}^{\infty\:}(\frac{2}{7})^{\frac{n}{2}}
y^{'''}+2y^{''}-y^'-2y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-y^{\prime\:}-2y=0
integral from 0 to 2 of sqrt(1+16x^2)	\int\:_{0}^{2}\sqrt{1+16x^{2}}dx
limit as x approaches pi of \sqrt[5]{(x-pi)/(x+pi)}	\lim\:_{x\to\:π}(\sqrt[5]{\frac{x-π}{x+π}})
simplify 2pisqrt(x/g)	simplify\:2π\sqrt{\frac{x}{g}}
derivative of (-ln(x+1)/(x^2))	\frac{d}{dx}(\frac{-\ln(x)+1}{x^{2}})
derivative of (x^2-3/x)	\frac{d}{dx}(\frac{x^{2}-3}{x})
integral of (5t^2)/2	\int\:\frac{5t^{2}}{2}dt
integral of (300)/(sqrt(2q+25))	\int\:\frac{300}{\sqrt{2q+25}}dq
limit as x approaches-5 of 10x+3	\lim\:_{x\to\:-5}(10x+3)
derivative of 4x-sin(2x)	\frac{d}{dx}(4x-\sin(2x))
integral of e^{x^2}*xln(x)	\int\:e^{x^{2}}\cdot\:x\ln(x)dx
integral of (tan^3(ln(x)))/(4x)	\int\:\frac{\tan^{3}(\ln(x))}{4x}dx
derivative of ln(sqrt(2))	derivative\:\ln(\sqrt{2})
(\partial)/(\partial x)(xyz+xy^3+yz^3+zx^3)	\frac{\partial\:}{\partial\:x}(xyz+xy^{3}+yz^{3}+zx^{3})
integral from 0 to 1 of (x-3)e^x	\int\:_{0}^{1}(x-3)e^{x}dx
derivative of f(x)=8x^5-8cos(x)	derivative\:f(x)=8x^{5}-8\cos(x)
derivative of x^{xcos(x})	\frac{d}{dx}(x^{x\cos(x)})
limit as x approaches 2 of 2x(x^2-3)	\lim\:_{x\to\:2}(2x(x^{2}-3))
(dy)/(dx)=(e^{x+y})/(y-1)	\frac{dy}{dx}=\frac{e^{x+y}}{y-1}
tangent of f(x)=3+4x^2-2x^3	tangent\:f(x)=3+4x^{2}-2x^{3}
f(x)=tan(sqrt(x))	f(x)=\tan(\sqrt{x})
integral of arccot(x)	\int\:\arccot(x)dx
y^'+2y=te^{-2t}	y^{\prime\:}+2y=te^{-2t}
x^2y^{''}+2xy^'+100.25y=0	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}+100.25y=0
derivative of f(x)=(ln(x))^2	derivative\:f(x)=(\ln(x))^{2}
y^{''}-4y=e^{2t}	y^{\prime\:\prime\:}-4y=e^{2t}
integral from 1/2 to 3 of 8xln(2x)	\int\:_{\frac{1}{2}}^{3}8x\ln(2x)dx
limit as t approaches 0 of ((tan(t)sec(2t)))/(3t)	\lim\:_{t\to\:0}(\frac{(\tan(t)\sec(2t))}{3t})
(\partial)/(\partial y)(xe^{xy}-2y+1)	\frac{\partial\:}{\partial\:y}(xe^{xy}-2y+1)
tangent of ln(x)	tangent\:\ln(x)
d/(d{x)}(({x}^2+{y}^2+{z}^2)^{1/2})	\frac{d}{d{x}}(({x}^{2}+{y}^{2}+{z}^{2})^{\frac{1}{2}})
derivative of 6ln(sec(x+tan(x)))	\frac{d}{dx}(6\ln(\sec(x)+\tan(x)))
derivative of cos^3(x)	derivative\:\cos^{3}(x)
y^'-6/x y=(y^4)/(x^{15)}	y^{\prime\:}-\frac{6}{x}y=\frac{y^{4}}{x^{15}}
derivative of-6sin(t)	derivative\:-6\sin(t)
derivative of ln(e^x+x)	derivative\:\ln(e^{x}+x)
4xy^'+y=20x	4xy^{\prime\:}+y=20x
integral of ((x^2-2x+5))/(x^2)	\int\:\frac{(x^{2}-2x+5)}{x^{2}}dx
limit as x approaches 0 of (ex-1)/x	\lim\:_{x\to\:0}(\frac{ex-1}{x})
derivative of-2xsin(x^2)	derivative\:-2x\sin(x^{2})
d/(d{x)}(arcsin^4({x}^7{y}^2+({z})/({x)^3}))	\frac{d}{d{x}}(\arcsin^{4}({x}^{7}{y}^{2}+\frac{{z}}{{x}^{3}}))
f^{''}(x)=x^3	f^{\prime\:\prime\:}(x)=x^{3}
integral of x/(sqrt(y+x^2))	\int\:\frac{x}{\sqrt{y+x^{2}}}dx
7sqrt(xy)(dy)/(dx)=4	7\sqrt{xy}\frac{dy}{dx}=4
integral of (2x+1)/(x-1)	\int\:\frac{2x+1}{x-1}dx
limit as x approaches infinity of 4^x	\lim\:_{x\to\:\infty\:}(4^{x})
(dy)/(dx)+(3/x)y=-x-5	\frac{dy}{dx}+(\frac{3}{x})y=-x-5
limit as x approaches 0 of (sin(1))/1	\lim\:_{x\to\:0}(\frac{\sin(1)}{1})
2(dy)/(dx)+y/x =x^2y^{-1}	2\frac{dy}{dx}+\frac{y}{x}=x^{2}y^{-1}
tangent of 9x+2x^2	tangent\:9x+2x^{2}
y(2y^2-3x^2)dx+(2x^3)dy=0	y(2y^{2}-3x^{2})dx+(2x^{3})dy=0
limit as x approaches-1+of 1/(1+x)	\lim\:_{x\to\:-1+}(\frac{1}{1+x})
derivative of 1/8 x-ln(2x)	\frac{d}{dx}(\frac{1}{8}x-\ln(2x))
derivative of f(x)=5sqrt(x)ln(x)	derivative\:f(x)=5\sqrt{x}\ln(x)
derivative of-3x^5+5x^3	\frac{d}{dx}(-3x^{5}+5x^{3})
derivative of y=t^3-2t+4	derivative\:y=t^{3}-2t+4
limit as x approaches 0 of ((2+x)^2+4)/x	\lim\:_{x\to\:0}(\frac{(2+x)^{2}+4}{x})
derivative of 1/(x(5+ln(x)))	derivative\:\frac{1}{x(5+\ln(x))}
(dy)/(dx)=2e^{(x-y)}	\frac{dy}{dx}=2e^{(x-y)}
tangent of 2x^3	tangent\:2x^{3}
derivative of-27	derivative\:-27
inverse oflaplace 1/(s(s^2+16))	inverselaplace\:\frac{1}{s(s^{2}+16)}
d/(ds)(1/(s^2+1))	\frac{d}{ds}(\frac{1}{s^{2}+1})
derivative of 4x^3e^{-x}	derivative\:4x^{3}e^{-x}
integral of cos^3(x/5)	\int\:\cos^{3}(\frac{x}{5})dx
tangent of f(x)=(x^3-16x)^{14},(4,0)	tangent\:f(x)=(x^{3}-16x)^{14},(4,0)
limit as x approaches 8 of 5	\lim\:_{x\to\:8}(5)
integral of e^{-y}	\int\:e^{-y}dy
tangent of 8x-x^2,\at x=1	tangent\:8x-x^{2},\at\:x=1
2y^'+y=0	2y^{\prime\:}+y=0
integral from-1 to 1 of t^2-2	\int\:_{-1}^{1}t^{2}-2dt
integral of 1/2 (2cos(θ))^2	\int\:\frac{1}{2}(2\cos(θ))^{2}dθ
integral of 200-x	\int\:200-xdx
integral from 0 to 6 of 2x-(x^2-4x)	\int\:_{0}^{6}2x-(x^{2}-4x)dx
limit as x approaches 0+of x^2	\lim\:_{x\to\:0+}(x^{2})
(\partial)/(\partial x)(x^2-10y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-10y^{2})
limit as x approaches 0 of 2^x-5^x	\lim\:_{x\to\:0}(2^{x}-5^{x})
derivative of (9x^6+8x^3)^4	derivative\:(9x^{6}+8x^{3})^{4}
y^'+7y=1	y^{\prime\:}+7y=1
integral of 1/(r^3)	\int\:\frac{1}{r^{3}}dr
integral of e^x(x+a+1)	\int\:e^{x}(x+a+1)dx
integral of 6x^2sin(3x)	\int\:6x^{2}\sin(3x)dx
sum from n=1 to infinity of 2-7/(8^n)	\sum\:_{n=1}^{\infty\:}2-\frac{7}{8^{n}}
integral of 3^{x+1}	\int\:3^{x+1}dx
limit as h approaches 0 of 1/h	\lim\:_{h\to\:0}(\frac{1}{h})
integral of 1/(sqrt(1+e^{4x))}	\int\:\frac{1}{\sqrt{1+e^{4x}}}dx
laplacetransform e^{-x}	laplacetransform\:e^{-x}

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