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Popular Calculus Problems

derivative of (1-cos(x))/(sin(x))	derivative\:\frac{1-\cos(x)}{\sin(x)}
y^'+(3x)/(x^2+4)y= x/(x^2+4),y(0)=1	y^{\prime\:}+\frac{3x}{x^{2}+4}y=\frac{x}{x^{2}+4},y(0)=1
integral of sin^2(8x)	\int\:\sin^{2}(8x)dx
integral of e^{-sqrt(x)}	\int\:e^{-\sqrt{x}}dx
derivative of (36/(x^2+2))	\frac{d}{dx}(\frac{36}{x^{2}+2})
derivative of 3/(sqrt(6x+3))	\frac{d}{dx}(\frac{3}{\sqrt{6x+3}})
integral of (x^3-4x+1)/(x^2-3x+2)	\int\:\frac{x^{3}-4x+1}{x^{2}-3x+2}dx
integral of sqrt(t^2+1)	\int\:\sqrt{t^{2}+1}dt
(dx)/(dt)=x-x^3	\frac{dx}{dt}=x-x^{3}
integral from 0 to infinity of e^{-2ax}	\int\:_{0}^{\infty\:}e^{-2ax}dx
limit as x approaches 9+of (x+8)/(x+9)	\lim\:_{x\to\:9+}(\frac{x+8}{x+9})
tangent of f(x)=(x-7)/(2x-3),\at x=1	tangent\:f(x)=\frac{x-7}{2x-3},\at\:x=1
integral of (arccos(x)-x)/(sqrt(1-x^2))	\int\:\frac{\arccos(x)-x}{\sqrt{1-x^{2}}}dx
integral from-0.5 to 4.5 of x^3	\int\:_{-0.5}^{4.5}x^{3}dx
integral of (x^2e^{-x})	\int\:(x^{2}e^{-x})dx
derivative of sqrt(4x+6)	\frac{d}{dx}(\sqrt{4x+6})
integral from-infinity to 0 of 1/(2-7x)	\int\:_{-\infty\:}^{0}\frac{1}{2-7x}dx
derivative of x^5ln(x)	derivative\:x^{5}\ln(x)
integral from 1 to x of sqrt(1+9t)	\int\:_{1}^{x}\sqrt{1+9t}dt
limit as n approaches infinity of nln(n)	\lim\:_{n\to\:\infty\:}(n\ln(n))
integral of xe^{8x}	\int\:xe^{8x}dx
tangent of x^{2/3}	tangent\:x^{\frac{2}{3}}
limit as x approaches 0 of ((4^x-2^x))/x	\lim\:_{x\to\:0}(\frac{(4^{x}-2^{x})}{x})
integral of (sin(x)+7cos(x)-1)	\int\:(\sin(x)+7\cos(x)-1)dx
derivative of csc^3(x^2)	\frac{d}{dx}(\csc^{3}(x^{2}))
derivative of (1+x^3^{2020})	\frac{d}{dx}((1+x^{3})^{2020})
slope of (8,8),(4,6)	slope\:(8,8),(4,6)
derivative of e^{2x}+2e^{2x}x	derivative\:e^{2x}+2e^{2x}x
(dy)/(dt)+ay=b	\frac{dy}{dt}+ay=b
tangent of 2sqrt(x)	tangent\:2\sqrt{x}
integral of x/(5x-4)	\int\:\frac{x}{5x-4}dx
integral of x(sqrt(a^2-x^2))	\int\:x(\sqrt{a^{2}-x^{2}})dx
limit as x approaches pi-of 4x	\lim\:_{x\to\:π-}(4x)
derivative of 500x-(x^2/(ln(x+300)))	\frac{d}{dx}(500x-\frac{x^{2}}{\ln(x+300)})
derivative of (3x^2-6x+10(x^3))	\frac{d}{dx}((3x^{2}-6x+10)(x^{3}))
y^{''}+2y^'+5y=e^{(-x)}sec(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=e^{(-x)}\sec(2x)
derivative of (12/(x^5)-7/(\sqrt[5]{x)})	\frac{d}{dx}(\frac{12}{x^{5}}-\frac{7}{\sqrt[5]{x}})
derivative of e^{x/y}ln((x^2/y))	\frac{d}{dx}(e^{\frac{x}{y}}\ln(\frac{x^{2}}{y}))
(xy-x)dx+(xy+y)dy=0	(xy-x)dx+(xy+y)dy=0
(dy)/(dx)=e^{2x-3y}	\frac{dy}{dx}=e^{2x-3y}
t^2y^{''}-8ty^'+8y=0	t^{2}y^{\prime\:\prime\:}-8ty^{\prime\:}+8y=0
derivative of sin(t^2)	derivative\:\sin(t^{2})
integral of te^{-i2pift}	\int\:te^{-i2πft}dt
derivative of f(x)=(3x-4)	derivative\:f(x)=(3x-4)
(y^2+1)dx=y(sec^2(x))dy	(y^{2}+1)dx=y(\sec^{2}(x))dy
(\partial)/(\partial x)(x-3y^2+4x^2y^3)	\frac{\partial\:}{\partial\:x}(x-3y^{2}+4x^{2}y^{3})
y^{''}-4y^'=6t	y^{\prime\:\prime\:}-4y^{\prime\:}=6t
inverse oflaplace (7s^3-9s+1)/(3s^5)	inverselaplace\:\frac{7s^{3}-9s+1}{3s^{5}}
(\partial)/(\partial z)(cos(xy))	\frac{\partial\:}{\partial\:z}(\cos(xy))
xyy^'-y^2=x^4	xyy^{\prime\:}-y^{2}=x^{4}
derivative of e^x*ln(x)	derivative\:e^{x}\cdot\:\ln(x)
integral of 17e^{-17x}	\int\:17e^{-17x}dx
limit as x approaches 0 of x(1+1/x)	\lim\:_{x\to\:0}(x(1+\frac{1}{x}))
derivative of 3cos(x)-2sin(x)	derivative\:3\cos(x)-2\sin(x)
sum from n=1 to infinity of e^{-4n}	\sum\:_{n=1}^{\infty\:}e^{-4n}
(\partial)/(\partial y)(ln(x-7y))	\frac{\partial\:}{\partial\:y}(\ln(x-7y))
integral of 1/(sqrt(3-2x))	\int\:\frac{1}{\sqrt{3-2x}}dx
(11+x^2)y^'-2xy=0	(11+x^{2})y^{\prime\:}-2xy=0
integral of 1/(8x^2-16x+64)	\int\:\frac{1}{8x^{2}-16x+64}dx
(\partial)/(\partial t)(se^t)	\frac{\partial\:}{\partial\:t}(se^{t})
f(x)=2^{3x^2-6}	f(x)=2^{3x^{2}-6}
(dP)/(dt)=5sqrt(Pt),P(1)=3	\frac{dP}{dt}=5\sqrt{Pt},P(1)=3
derivative of x/(4.5c(c-x))	\frac{d}{dx}(\frac{x}{4.5c}(c-x))
limit as t approaches 6 of 8(t-5)(t-7)	\lim\:_{t\to\:6}(8(t-5)(t-7))
derivative of (x+3/x /(sqrt(x)))	\frac{d}{dx}(\frac{x+\frac{3}{x}}{\sqrt{x}})
integral of (x^2+1)	\int\:(x^{2}+1)dx
derivative of cot(9(1-2x^2))	\frac{d}{dx}(\cot(9)(1-2x^{2}))
integral of ln(sqrt(x^2-4))	\int\:\ln(\sqrt{x^{2}-4})dx
derivative of 1/(9x^{8/9)}	derivative\:\frac{1}{9x^{\frac{8}{9}}}
derivative of 1/2 cos^2(5x)	\frac{d}{dx}(\frac{1}{2}\cos^{2}(5x))
derivative of tan(3x-x^2)	\frac{d}{dx}(\tan(3x-x^{2}))
(dy)/(dx)= 1/(xsin(y)+2sin(2y))	\frac{dy}{dx}=\frac{1}{x\sin(y)+2\sin(2y)}
integral of x/(sqrt(x^2))	\int\:\frac{x}{\sqrt{x^{2}}}dx
x^2y^'+xy=3y^3	x^{2}y^{\prime\:}+xy=3y^{3}
integral of 54sec^4(x)	\int\:54\sec^{4}(x)dx
derivative of 3y	derivative\:3y
integral from 0 to 1 of x^{10}+10^x	\int\:_{0}^{1}x^{10}+10^{x}dx
integral of 6xe^{7x}	\int\:6xe^{7x}dx
integral of sin^3(x)cos^4(x)	\int\:\sin^{3}(x)\cos^{4}(x)dx
integral of 1/(1+x^4)	\int\:\frac{1}{1+x^{4}}dx
area 4x^2-3,-x^2+9	area\:4x^{2}-3,-x^{2}+9
integral of 1/(sqrt(7-x^2))	\int\:\frac{1}{\sqrt{7-x^{2}}}dx
derivative of 1/4 cos^4(x^3-sin^2(6x))	\frac{d}{dx}(\frac{1}{4}\cos^{4}(x^{3})-\sin^{2}(6x))
integral of xsinh(2x)	\int\:x\sinh(2x)dx
derivative of 15e^x	derivative\:15e^{x}
derivative of-1/(3\sqrt[5]{7cos(2x)})	\frac{d}{dx}(-\frac{1}{3\sqrt[5]{7\cos(2x)}})
derivative of (5x+3^4)	\frac{d}{dx}((5x+3)^{4})
derivative of (arctan(7x)^2)	\frac{d}{dx}((\arctan(7x))^{2})
limit as x approaches a of (\sqrt[3]{x}-\sqrt[3]{a})/(x^2-a^2)	\lim\:_{x\to\:a}(\frac{\sqrt[3]{x}-\sqrt[3]{a}}{x^{2}-a^{2}})
sum from y=0 to infinity of 2^{-2-y+x}	\sum\:_{y=0}^{\infty\:}2^{-2-y+x}
(\partial)/(\partial y)(xsqrt(1+y^5))	\frac{\partial\:}{\partial\:y}(x\sqrt{1+y^{5}})
integral of te^{-at}	\int\:te^{-at}dt
6t^2y^{''}-12y=14t^2-1	6t^{2}y^{\prime\:\prime\:}-12y=14t^{2}-1
integral of 4x^3-10x	\int\:4x^{3}-10xdx
integral of (4t^3-t^2+16t)/(t^2+4)	\int\:\frac{4t^{3}-t^{2}+16t}{t^{2}+4}dt
y^'-2xy=8x	y^{\prime\:}-2xy=8x
derivative of e^{-x}cos(3x)	\frac{d}{dx}(e^{-x}\cos(3x))
integral from 1 to 3 of sqrt(t)ln(t)	\int\:_{1}^{3}\sqrt{t}\ln(t)dt
integral of x*cos(x)	\int\:x\cdot\:\cos(x)dx
derivative of ln(x^3+e^{2x})	\frac{d}{dx}(\ln(x^{3})+e^{2x})

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