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Popular Calculus Problems

integral of sin^{2020}(x	\int\:\sin^{2020}(d)xdx
integral of x\sqrt[3]{(x+3)^5}	\int\:x\sqrt[3]{(x+3)^{5}}dx
derivative of-sin(3x3)	\frac{d}{dx}(-\sin(3x)3)
integral of (2x+1)^{-1}	\int\:(2x+1)^{-1}dx
limit as x approaches+0 of (2sin(2x))/x	\lim\:_{x\to\:+0}(\frac{2\sin(2x)}{x})
integral of (x^2)/(sqrt(x^3+4))	\int\:\frac{x^{2}}{\sqrt{x^{3}+4}}dx
10y^{''}-7y^'-12y=0	10y^{\prime\:\prime\:}-7y^{\prime\:}-12y=0
limit as x approaches 2-of x+3	\lim\:_{x\to\:2-}(x+3)
4y^{''}-12y^'+9y=0,y(1)=-2,y^'(-2)=-3	4y^{\prime\:\prime\:}-12y^{\prime\:}+9y=0,y(1)=-2,y^{\prime\:}(-2)=-3
integral of (sqrt(x))/(1+x^3)	\int\:\frac{\sqrt{x}}{1+x^{3}}dx
(d^2y)/(dx^2)+2(dy)/(dx)-y=20xe^x	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}-y=20xe^{x}
(dy)/(dx)+y=x	\frac{dy}{dx}+y=x
normal of f(x)=2x^2-5,(2,-2)	normal\:f(x)=2x^{2}-5,(2,-2)
derivative of ln(x+ln(sin(y)))	\frac{d}{dx}(\ln(x)+\ln(\sin(y)))
derivative of-7x	\frac{d}{dx}(-7x)
(x+1)(dy)/(dx)+y=ln(x),y(1)=15	(x+1)\frac{dy}{dx}+y=\ln(x),y(1)=15
integral of 1/(\sqrt[3]{x)}	\int\:\frac{1}{\sqrt[3]{x}}dx
derivative of (x^2-1)/(x^2+4)	derivative\:\frac{x^{2}-1}{x^{2}+4}
integral of (ln(x+4))/(x+4)	\int\:\frac{\ln(x+4)}{x+4}dx
integral of (sec(y)tan(y)-csc(y)cot(y))	\int\:(\sec(y)\tan(y)-\csc(y)\cot(y))dy
area y=sqrt(1+5x),1<= x<= 7	area\:y=\sqrt{1+5x},1\le\:x\le\:7
integral of ln(x)+x	\int\:\ln(x)+xdx
integral of sin^3(18x)	\int\:\sin^{3}(18x)dx
derivative of g(t)=(9t+5)^2(5t-6)^{-3}	derivative\:g(t)=(9t+5)^{2}(5t-6)^{-3}
(3x+2)+(3y-3)y^'=0	(3x+2)+(3y-3)y^{\prime\:}=0
integral of y(y+1)e^{-2y}	\int\:y(y+1)e^{-2y}dy
integral of e+e^{3x}	\int\:e+e^{3x}dx
derivative of x^{-2}e^{2x}	\frac{d}{dx}(x^{-2}e^{2x})
integral of-1/((x+1)^2)	\int\:-\frac{1}{(x+1)^{2}}dx
derivative of x/(tan(x))	\frac{d}{dx}(\frac{x}{\tan(x)})
inverse oflaplace (2e^{-2s})/(s(s+2)(s+3)^2)	inverselaplace\:\frac{2e^{-2s}}{s(s+2)(s+3)^{2}}
limit as x approaches a of 2f(x)-3g(x)	\lim\:_{x\to\:a}(2f(x)-3g(x))
derivative of (sqrt(x^2+a^2)^{e^{x^2}})	\frac{d}{dx}((\sqrt{x^{2}+a^{2}})^{e^{x^{2}}})
d/(dy)((-y)/(x^2+y^2))	\frac{d}{dy}(\frac{-y}{x^{2}+y^{2}})
derivative of log_{2}(3x+1)	\frac{d}{dx}(\log_{2}(3x+1))
xy^'+y=x	xy^{\prime\:}+y=x
derivative of ((-5x+1^3)/((3x-3)^6))	\frac{d}{dx}(\frac{(-5x+1)^{3}}{(3x-3)^{6}})
(\partial)/(\partial x)(x^2-y^2-2z^2)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}-2z^{2})
derivative of (12x^5+8x^3-2x^2/(4x^2))	\frac{d}{dx}(\frac{12x^{5}+8x^{3}-2x^{2}}{4x^{2}})
derivative of 8/(e^x+e^{-x)}	derivative\:\frac{8}{e^{x}+e^{-x}}
taylor e^{-6x},0	taylor\:e^{-6x},0
integral of sqrt(x)ln(5x)	\int\:\sqrt{x}\ln(5x)dx
limit as x approaches 2-of sqrt(6-3x)-3	\lim\:_{x\to\:2-}(\sqrt{6-3x}-3)
integral from 0 to 1 of 2x(8-x^2)	\int\:_{0}^{1}2x(8-x^{2})dx
limit as x approaches-3 of-3x	\lim\:_{x\to\:-3}(-3x)
(\partial)/(\partial x)(x^3-2xy^2-y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-2xy^{2}-y^{3})
integral from 0 to 0.5 of (200x)	\int\:_{0}^{0.5}(200x)dx
simplify 1/(sqrt(u))	simplify\:\frac{1}{\sqrt{u}}
inverse oflaplace 2/(s(s^2+4s+6))	inverselaplace\:\frac{2}{s(s^{2}+4s+6)}
integral of (9x^8+10x^5-5x^2-5)	\int\:(9x^{8}+10x^{5}-5x^{2}-5)dx
integral of e^{-3x}+ln(3)-1/x	\int\:e^{-3x}+\ln(3)-\frac{1}{x}dx
(dy)/(dx)=-((2x^2+y))/((x^2y-x))	\frac{dy}{dx}=-\frac{(2x^{2}+y)}{(x^{2}y-x)}
(\partial)/(\partial x)(e^tcos(x))	\frac{\partial\:}{\partial\:x}(e^{t}\cos(x))
derivative of 7x^3+5x^2+4x	derivative\:7x^{3}+5x^{2}+4x
(\partial)/(\partial x)(cos(x+6y))	\frac{\partial\:}{\partial\:x}(\cos(x+6y))
integral of (2x^3-3x^2+1)/(x^2)	\int\:\frac{2x^{3}-3x^{2}+1}{x^{2}}dx
d/(dt)(cos^2(t))	\frac{d}{dt}(\cos^{2}(t))
(dy)/(dx)=(x+1)/((x^2+2x-3)^2)	\frac{dy}{dx}=\frac{x+1}{(x^{2}+2x-3)^{2}}
d/(dt)(9cos(t)-cos(9t))	\frac{d}{dt}(9\cos(t)-\cos(9t))
integral of e^{(4x)/3}(4/3)	\int\:e^{\frac{4x}{3}}(\frac{4}{3})dx
derivative of-(3y)/(3x+2y)	derivative\:-\frac{3y}{3x+2y}
integral of 41tan^5(x)sec^4(x)	\int\:41\tan^{5}(x)\sec^{4}(x)dx
limit as x approaches 6 of (x-6)/(x^2-x)	\lim\:_{x\to\:6}(\frac{x-6}{x^{2}-x})
(d^2y)/(dx^2)+2(dy)/(dx)+2y=0	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+2y=0
f(x)=\sqrt[3]{x+1}	f(x)=\sqrt[3]{x+1}
integral of e^{2x+3}	\int\:e^{2x+3}dx
derivative of x^2-2x-2sin(x-2)	\frac{d}{dx}(x^{2}-2x-2\sin(x-2))
integral of (sin(6e^{-2x}))/(e^{2x)}	\int\:\frac{\sin(6e^{-2x})}{e^{2x}}dx
integral from 1 to 9 of 1/(8-sqrt(x))	\int\:_{1}^{9}\frac{1}{8-\sqrt{x}}dx
integral of (x^3-2)/(x+1)	\int\:\frac{x^{3}-2}{x+1}dx
integral of 2x+8	\int\:2x+8dx
integral of 6x^2e^x	\int\:6x^{2}e^{x}dx
integral of u/(u-1)	\int\:\frac{u}{u-1}du
derivative of f(x)=xcos(x)sin(x)	derivative\:f(x)=x\cos(x)\sin(x)
integral from 0 to 1 of 1/(t^2+2)	\int\:_{0}^{1}\frac{1}{t^{2}+2}dt
x^4+y^3sqrt(x^5+4)(dy)/(dx)=0	x^{4}+y^{3}\sqrt{x^{5}+4}\frac{dy}{dx}=0
integral of (sin(3x))/(cos^3(3x))	\int\:\frac{\sin(3x)}{\cos^{3}(3x)}dx
integral of 1/(6x^7)	\int\:\frac{1}{6x^{7}}dx
derivative of 4sqrt(x+1)	\frac{d}{dx}(4\sqrt{x+1})
integral of 3x^{sqrt(3)}	\int\:3x^{\sqrt{3}}dx
integral from-infinity to infinity of 47cos(pix)	\int\:_{-\infty\:}^{\infty\:}47\cos(πx)dx
limit as n approaches infinity of (1+sin(1/n))^{sqrt(n)}	\lim\:_{n\to\:\infty\:}((1+\sin(\frac{1}{n}))^{\sqrt{n}})
derivative of f(x)=x^2-8x-91	derivative\:f(x)=x^{2}-8x-91
tangent of f(x)= 1/(x+1),\at x=0	tangent\:f(x)=\frac{1}{x+1},\at\:x=0
integral of 2cos(x)sin^2(x)	\int\:2\cos(x)\sin^{2}(x)dx
derivative of sqrt(x+1)	derivative\:\sqrt{x+1}
inverse oflaplace (4s+7)/(s^2-4)	inverselaplace\:\frac{4s+7}{s^{2}-4}
(y+1)((dy)/(dx))=2x	(y+1)(\frac{dy}{dx})=2x
y^{''}-7y^'+12y=0,y(0)=-1/2 ,y^'(0)=-9/4	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=0,y(0)=-\frac{1}{2},y^{\prime\:}(0)=-\frac{9}{4}
integral of (15e^{5y})/(e^{5y)+2}	\int\:\frac{15e^{5y}}{e^{5y}+2}dy
tangent of x^3+y^3=8xy,(4,4)	tangent\:x^{3}+y^{3}=8xy,(4,4)
limit as x approaches 3 of 10^{x^2-3*x}	\lim\:_{x\to\:3}(10^{x^{2}-3\cdot\:x})
(\partial)/(\partial y)(xe^{9xy})	\frac{\partial\:}{\partial\:y}(xe^{9xy})
area x+2,x^2-4	area\:x+2,x^{2}-4
(\partial)/(\partial x)(3y^2)	\frac{\partial\:}{\partial\:x}(3y^{2})
integral of e^r(2+3e^r)^{3/2}	\int\:e^{r}(2+3e^{r})^{\frac{3}{2}}dr
integral of cos(wnt)	\int\:\cos(wnt)dt
derivative of y-5ln\|y\|+xy	\frac{d}{dx}(y-5\ln\left\|y\right\|+xy)
derivative of-(2x)/y	derivative\:-\frac{2x}{y}
integral from 1 to 2 of 5/(x^3+4x)	\int\:_{1}^{2}\frac{5}{x^{3}+4x}dx

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