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Popular Calculus Problems

y^'=-2xy^3	y^{\prime\:}=-2xy^{3}
limit as x approaches (3pi)/2 of sec(x)	\lim\:_{x\to\:\frac{3π}{2}}(\sec(x))
limit as x approaches 0 of (x^3)/(ln\|x\|)	\lim\:_{x\to\:0}(\frac{x^{3}}{\ln\left\|x\right\|})
y^'=y(xy^3+5)	y^{\prime\:}=y(xy^{3}+5)
integral of (e^u)/((7-e^u)^2)	\int\:\frac{e^{u}}{(7-e^{u})^{2}}du
(x^2+1)dy=(x^3-2xy+x)dx	(x^{2}+1)dy=(x^{3}-2xy+x)dx
derivative of arccos(sqrt(x))	derivative\:\arccos(\sqrt{x})
integral of 5sin^4(r)cos(r)	\int\:5\sin^{4}(r)\cos(r)dr
derivative of (e^x)/(x^2)	derivative\:\frac{e^{x}}{x^{2}}
derivative of (x-a^3(x-b))	\frac{d}{dx}((x-a)^{3}(x-b))
(\partial)/(\partial y)(x^4+3x^2y)	\frac{\partial\:}{\partial\:y}(x^{4}+3x^{2}y)
derivative of 3x^2cos(3x)	derivative\:3x^{2}\cos(3x)
(\partial)/(\partial x)(5xy-3x^2y)	\frac{\partial\:}{\partial\:x}(5xy-3x^{2}y)
integral of x^4cos(x^5)	\int\:x^{4}\cos(x^{5})dx
limit as x approaches 2 of 2/x+4	\lim\:_{x\to\:2}(\frac{2}{x}+4)
integral from 0 to 4 of 2/(sqrt(x))	\int\:_{0}^{4}\frac{2}{\sqrt{x}}dx
integral of (7e^{9x})	\int\:(7e^{9x})dx
derivative of 5^{tan(5x)}	derivative\:5^{\tan(5x)}
integral of 1/(1-2x+x^2)	\int\:\frac{1}{1-2x+x^{2}}dx
integral of e^{-2x}sin(4x)	\int\:e^{-2x}\sin(4x)dx
laplacetransform 6(t-4)	laplacetransform\:6(t-4)
(\partial)/(\partial x)(e^{1/x})	\frac{\partial\:}{\partial\:x}(e^{\frac{1}{x}})
integral of (x+1)/(x^2+x+1)	\int\:\frac{x+1}{x^{2}+x+1}dx
(dy)/(dt)+3y=11,y(0)=1	\frac{dy}{dt}+3y=11,y(0)=1
integral of (-4x)/(2x+1)	\int\:\frac{-4x}{2x+1}dx
y^{''}-2y^'+2y=6	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=6
limit as x approaches infinity of 1-1/x	\lim\:_{x\to\:\infty\:}(1-\frac{1}{x})
integral of e^{-st}cos(at)	\int\:e^{-st}\cos(at)dt
integral of 2/(xsqrt(1+2x))	\int\:\frac{2}{x\sqrt{1+2x}}dx
integral of 1/(sqrt(t^2-2t+37))	\int\:\frac{1}{\sqrt{t^{2}-2t+37}}dt
integral from 0 to pi/4 of 7sec^2(x)	\int\:_{0}^{\frac{π}{4}}7\sec^{2}(x)dx
derivative of 3(2xe^x+e^xx^2)	\frac{d}{dx}(3(2xe^{x}+e^{x}x^{2}))
y^'=(y^2)/(t^3)	y^{\prime\:}=\frac{y^{2}}{t^{3}}
derivative of ln(xe^{-6x})	derivative\:\ln(xe^{-6x})
simplify (sec(θ))/(1+sec(θ))	simplify\:\frac{\sec(θ)}{1+\sec(θ)}
integral of (7x^2+3x+4)/(x^3-x)	\int\:\frac{7x^{2}+3x+4}{x^{3}-x}dx
taylor 2/(3x+1),2	taylor\:\frac{2}{3x+1},2
(\partial)/(\partial x)(cos(y)e^{xy}+e^{xy}sin(y)x)	\frac{\partial\:}{\partial\:x}(\cos(y)e^{xy}+e^{xy}\sin(y)x)
limit as x approaches 0 of 4/(x-1)	\lim\:_{x\to\:0}(\frac{4}{x-1})
integral of (xe^{x^2})/(1+e^{x^2)}	\int\:\frac{xe^{x^{2}}}{1+e^{x^{2}}}dx
derivative of f(x)=2x^2-4x	derivative\:f(x)=2x^{2}-4x
derivative of f(x)x^2+8x-2	derivative\:f(x)x^{2}+8x-2
integral from 1 to 10 of 1/x	\int\:_{1}^{10}\frac{1}{x}dx
derivative of-arctan(x)	derivative\:-\arctan(x)
integral of (xe^{5x})/((5x+1)^2)	\int\:\frac{xe^{5x}}{(5x+1)^{2}}dx
limit as x approaches 0 of e^{(\|x\|)/x}	\lim\:_{x\to\:0}(e^{\frac{\left\|x\right\|}{x}})
maclaurin cos^2(x)	maclaurin\:\cos^{2}(x)
(x^2-y^2)((dy)/(dx))=2xy	(x^{2}-y^{2})(\frac{dy}{dx})=2xy
derivative of (sin(x)/(sqrt(1+x^2)))	\frac{d}{dx}(\frac{\sin(x)}{\sqrt{1+x^{2}}})
integral of sin(pit)cos(pit)	\int\:\sin(πt)\cos(πt)dt
derivative of 16e^{4x}	\frac{d}{dx}(16e^{4x})
derivative of x/3-3/x	\frac{d}{dx}(\frac{x}{3}-\frac{3}{x})
(x+1)(dy)/(dx)+y=ln(x)	(x+1)\frac{dy}{dx}+y=\ln(x)
integral from 0 to 2 of 4^{-x}	\int\:_{0}^{2}4^{-x}dx
y^'= 1/(x+y)	y^{\prime\:}=\frac{1}{x+y}
derivative of (3x^2-4x^2)	\frac{d}{dx}((3x^{2}-4x)^{2})
derivative of x^2+3x+1	derivative\:x^{2}+3x+1
inverse oflaplace f(t)=7t+3	inverselaplace\:f(t)=7t+3
derivative of \sqrt[3]{x-1}	\frac{d}{dx}(\sqrt[3]{x-1})
integral of 1/(xsqrt(1-x^2))	\int\:\frac{1}{x\sqrt{1-x^{2}}}dx
derivative of f(x)=(1-3x)/(6+x)	derivative\:f(x)=\frac{1-3x}{6+x}
limit as x approaches-1+of (\|x+1\|)/(x-1)	\lim\:_{x\to\:-1+}(\frac{\left\|x+1\right\|}{x-1})
(dy)/(dx)=((3y+10507))/(x-12),y(0)=47	\frac{dy}{dx}=\frac{(3y+10507)}{x-12},y(0)=47
derivative of y=arcsec(x)	derivative\:y=\arcsec(x)
t(dy)/(dt)+2y=t^{-3}	t\frac{dy}{dt}+2y=t^{-3}
integral from 0 to pi of e^xsin(x)	\int\:_{0}^{π}e^{x}\sin(x)dx
limit as x approaches+0 of (sin(x))/(4x)	\lim\:_{x\to\:+0}(\frac{\sin(x)}{4x})
derivative of 1500x+3000(4x+3)^{-1}-1000	derivative\:1500x+3000(4x+3)^{-1}-1000
derivative of f(x^2)=x^4	\frac{d}{dx}(f(x^{2}))=x^{4}
(d^2y)/(dθ^2)+y=0	\frac{d^{2}y}{dθ^{2}}+y=0
integral of (x^2-2)(x^3-6x)^{207}	\int\:(x^{2}-2)(x^{3}-6x)^{207}dx
limit as x approaches 2 of 3x^2	\lim\:_{x\to\:2}(3x^{2})
(\partial)/(\partial x)(-x-6y)	\frac{\partial\:}{\partial\:x}(-x-6y)
slope of y= 1/x	slope\:y=\frac{1}{x}
integral of x^2*(1+sqrt(x))	\int\:x^{2}\cdot\:(1+\sqrt{x})dx
derivative of 1/((2x-1^3))	\frac{d}{dx}(\frac{1}{(2x-1)^{3}})
integral of (9te^t,ln(t))	\int\:(9te^{t},\ln(t))dt
derivative of (sec(x)/(tan(x)))	\frac{d}{dx}(\frac{\sec(x)}{\tan(x)})
6y^{''}+4y^'=0	6y^{\prime\:\prime\:}+4y^{\prime\:}=0
limit as x approaches 5-of (5-x)^{2/3}	\lim\:_{x\to\:5-}((5-x)^{\frac{2}{3}})
integral of-7/x	\int\:-\frac{7}{x}dx
limit as x approaches 4 of x^3-64	\lim\:_{x\to\:4}(x^{3}-64)
(\partial)/(\partial x)(x^2*y^2)	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:y^{2})
inverse oflaplace (0.5)/(s+1)	inverselaplace\:\frac{0.5}{s+1}
integral of (ln(2x))/x	\int\:\frac{\ln(2x)}{x}dx
integral of 5sin^4(x)cos(x)	\int\:5\sin^{4}(x)\cos(x)dx
integral of x^3sqrt(196-x^2)	\int\:x^{3}\sqrt{196-x^{2}}dx
derivative of a^xln(a)	\frac{d}{dx}(a^{x}\ln(a))
f(x)=-5x+2	f(x)=-5x+2
limit as x approaches 0 of (sin(x^6))/x	\lim\:_{x\to\:0}(\frac{\sin(x^{6})}{x})
integral from 0 to 2 of 3e^{-2x}	\int\:_{0}^{2}3e^{-2x}dx
derivative of x^5-5x^3+4x	\frac{d}{dx}(x^{5}-5x^{3}+4x)
derivative of e^{8x^2}	derivative\:e^{8x^{2}}
derivative of (2x-x^2^2+9)	\frac{d}{dx}((2x-x^{2})^{2}+9)
integral of (x-2)ln(x)	\int\:(x-2)\ln(x)dx
tangent of 4x^2+y^2=25,(2,3)	tangent\:4x^{2}+y^{2}=25,(2,3)
derivative of 70x^{-5}	derivative\:70x^{-5}
integral of (x^2)/((a+bx^3)^2)	\int\:\frac{x^{2}}{(a+bx^{3})^{2}}dx
limit as x approaches 0+of (tan(7x))^x	\lim\:_{x\to\:0+}((\tan(7x))^{x})
(2y^2+3x)dx+4xydy=0	(2y^{2}+3x)dx+4xydy=0

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