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Popular Calculus Problems

integral of 1/(x+8)	\int\:\frac{1}{x+8}dx
integral from 0 to 1 of (2x)/((x^2+5)^2)	\int\:_{0}^{1}\frac{2x}{(x^{2}+5)^{2}}dx
integral from 0 to pi/4 of (sin(x))^4	\int\:_{0}^{\frac{π}{4}}(\sin(x))^{4}dx
integral of (3u^{-2}-4u^2+1)	\int\:(3u^{-2}-4u^{2}+1)du
integral of (3x-2)^{20}	\int\:(3x-2)^{20}dx
tangent of f(x)=-6sqrt(x),\at x=4	tangent\:f(x)=-6\sqrt{x},\at\:x=4
integral of 3sin^4(x)	\int\:3\sin^{4}(x)dx
tangent of x^4-3x^2+2	tangent\:x^{4}-3x^{2}+2
derivative of cos(x^2+2x)	\frac{d}{dx}(\cos(x^{2}+2x))
derivative of (8x^2+4x+4)/(sqrt(x))	derivative\:\frac{8x^{2}+4x+4}{\sqrt{x}}
area x=y^2+6y,x=y	area\:x=y^{2}+6y,x=y
integral from 0 to x of 4tan(t)	\int\:_{0}^{x}4\tan(t)dt
y^{''}+9y=e^{3x}	y^{\prime\:\prime\:}+9y=e^{3x}
(\partial)/(\partial x)(sin^2(xy))	\frac{\partial\:}{\partial\:x}(\sin^{2}(xy))
121y^{''}+44y^'+4y=0	121y^{\prime\:\prime\:}+44y^{\prime\:}+4y=0
inverse oflaplace 1/(s(s^2+4))	inverselaplace\:\frac{1}{s(s^{2}+4)}
limit as x approaches 7/8 of (x)^4	\lim\:_{x\to\:\frac{7}{8}}((x)^{4})
limit as x approaches 3+of 6/(x-3)	\lim\:_{x\to\:3+}(\frac{6}{x-3})
tangent of f(x)=6e^xcos(x),\at x=0	tangent\:f(x)=6e^{x}\cos(x),\at\:x=0
laplacetransform sin(2x)cos(2x)	laplacetransform\:\sin(2x)\cos(2x)
derivative of 50e^{4x}+300e^{-3x}	\frac{d}{dx}(50e^{4x}+300e^{-3x})
(\partial)/(\partial x)(x^2e^y)	\frac{\partial\:}{\partial\:x}(x^{2}e^{y})
derivative of e^{4tsin(2t)}	derivative\:e^{4t\sin(2t)}
integral of (x^2+3)/(x^2-3x+2)	\int\:\frac{x^{2}+3}{x^{2}-3x+2}dx
integral of (3x^2+cos(x))	\int\:(3x^{2}+\cos(x))dx
derivative of e^{3xsin(2x})	\frac{d}{dx}(e^{3x\sin(2x)})
(\partial)/(\partial x)(x/(1+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{1+x^{2}y^{2}})
integral of x(x+7)^6	\int\:x(x+7)^{6}dx
derivative of (x^2-5x+3/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}-5x+3}{\sqrt{x}})
derivative of 4x^2+5x+3	\frac{d}{dx}(4x^{2}+5x+3)
integral of (4y)/x	\int\:\frac{4y}{x}dx
(\partial)/(\partial y)(xye^{-6y})	\frac{\partial\:}{\partial\:y}(xye^{-6y})
derivative of ln((e^x+1/(e^x-1)))	\frac{d}{dx}(\ln(\frac{e^{x}+1}{e^{x}-1}))
d/(dθ)(ln({x}(θ))(-θ-2))	\frac{d}{dθ}(\ln({x}(θ))(-θ-2))
integral of-csc^2((9x)/8)	\int\:-\csc^{2}(\frac{9x}{8})dx
integral of e^u	\int\:e^{u}du
9x^2y^'=y^'+7xe^{-y}	9\cdot\:x^{2}\cdot\:y^{\prime\:}=y^{\prime\:}+7\cdot\:x\cdot\:e^{-y}
derivative of f(x)=6x^{4/3}-2/3 x^{3/2}+x^2-7x+1	derivative\:f(x)=6x^{\frac{4}{3}}-\frac{2}{3}x^{\frac{3}{2}}+x^{2}-7x+1
derivative of cos^2(x/2)	\frac{d}{dx}(\cos^{2}(\frac{x}{2}))
y^{''}-2y^'-3y=e^{-t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=e^{-t}
derivative of (e^{2x}-e^x+1/(e^x))	\frac{d}{dx}(\frac{e^{2x}-e^{x}+1}{e^{x}})
integral from 0 to 1 of 11xsqrt(x^2+36)	\int\:_{0}^{1}11x\sqrt{x^{2}+36}dx
xy^'+2y^'-(x+2)sin(x)+y=0	xy^{\prime\:}+2y^{\prime\:}-(x+2)\sin(x)+y=0
(\partial)/(\partial x)((x^2y-y^3)^5)	\frac{\partial\:}{\partial\:x}((x^{2}y-y^{3})^{5})
inverse oflaplace-(e^{(-2s)})/((s^2-4s+4))	inverselaplace\:-\frac{e^{(-2s)}}{(s^{2}-4s+4)}
integral of x^5e^{4x}	\int\:x^{5}e^{4x}dx
derivative of tan(x+xsec^2(x))	\frac{d}{dx}(\tan(x)+x\sec^{2}(x))
derivative of sin(tan(x)+sec(x))	derivative\:\sin(\tan(x)+\sec(x))
derivative of cos(5x-pi/2)	\frac{d}{dx}(\cos(5x-\frac{π}{2}))
inverse oflaplace s/(s^2-s+1)	inverselaplace\:\frac{s}{s^{2}-s+1}
inverse oflaplace 3/(s(s+3))	inverselaplace\:\frac{3}{s(s+3)}
tangent of x^2+3x	tangent\:x^{2}+3x
(\partial)/(\partial x)(x^2y^3+xy-2)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+xy-2)
integral from ln(4) to ln(9) of e^{x/2}	\int\:_{\ln(4)}^{\ln(9)}e^{\frac{x}{2}}dx
derivative of f(x)=sin(1/(x^2))	derivative\:f(x)=\sin(\frac{1}{x^{2}})
integral of (cos^6(x))/(sin^{10)(x)}	\int\:\frac{\cos^{6}(x)}{\sin^{10}(x)}dx
y^{''}+(a_{1^2}pi^2)/(a_{2)^2}a_{3}^2y=0	y^{\prime\:\prime\:}+\frac{a_{1^{2}}π^{2}}{a_{2}^{2}}a_{3}^{2}y=0
inverse oflaplace sin(s)	inverselaplace\:\sin(s)
integral of-e^x+sin(2x)	\int\:-e^{x}+\sin(2x)dx
integral from 0 to 3 of cos((nxpi)/3)	\int\:_{0}^{3}\cos(\frac{nxπ}{3})dx
derivative of (x-1/(x+2))	\frac{d}{dx}(\frac{x-1}{x+2})
(\partial)/(\partial x)(x/4+sqrt(y))	\frac{\partial\:}{\partial\:x}(\frac{x}{4}+\sqrt{y})
(\partial)/(\partial x)(b)	\frac{\partial\:}{\partial\:x}(b)
derivative of xl	\frac{d}{dx}(xl)
taylor 1/(sqrt(1-x^2))	taylor\:\frac{1}{\sqrt{1-x^{2}}}
limit as x approaches infinity of 2x	\lim\:_{x\to\:\infty\:}(2x)
derivative of (2xln(x-x)/(ln^2(x)))	\frac{d}{dx}(\frac{2x\ln(x)-x}{\ln^{2}(x)})
derivative of e^{1/({f(x)}})	\frac{d}{dx}(e^{\frac{1}{{f}(x)}})
integral of 1/(5^x)	\int\:\frac{1}{5^{x}}dx
(dy)/(dx)+2xy=2x	\frac{dy}{dx}+2xy=2x
inverse oflaplace 1/(s^2-3s+5)	inverselaplace\:\frac{1}{s^{2}-3s+5}
y^'=((4t^3+1))/((2y-6))	y^{\prime\:}=\frac{(4t^{3}+1)}{(2y-6)}
limit as x approaches-1 of (2x)/(\|x\|)	\lim\:_{x\to\:-1}(\frac{2x}{\left\|x\right\|})
integral of (e^{x^{1/2}})/(x^3)	\int\:\frac{e^{x^{\frac{1}{2}}}}{x^{3}}dx
integral of (-2T+x)e^{-iz*x}	\int\:(-2T+x)\cdot\:e^{-i\cdot\:z\cdot\:x}dx
laplacetransform (t^2)(sin(2t))	laplacetransform\:(t^{2})\cdot\:(\sin(2\cdot\:t))
limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25)	\lim\:_{x\to\:25}(\frac{\frac{1}{\sqrt{x}}-\frac{1}{5}}{x-25})
(d^2y)/(dx^2)-y=10sin^2(x)	\frac{d^{2}y}{dx^{2}}-y=10\sin^{2}(x)
derivative of sin(x^{ln(x}))	\frac{d}{dx}(\sin(x^{\ln(x)}))
derivative of y=4sqrt(9-x^2)	derivative\:y=4\sqrt{9-x^{2}}
derivative of (x^2-1^{-1})	\frac{d}{dx}((x^{2}-1)^{-1})
derivative of f(x)=sqrt(9-16x)	derivative\:f(x)=\sqrt{9-16x}
integral of (8x^7+9)sqrt(x^8+9x)	\int\:(8x^{7}+9)\sqrt{x^{8}+9x}dx
tangent of y= 8/(x^2)	tangent\:y=\frac{8}{x^{2}}
derivative of 16e^{2x}	\frac{d}{dx}(16e^{2x})
derivative of y=3arccos(x/2)	derivative\:y=3\arccos(\frac{x}{2})
(dy)/(dx)=(4sec(y))/((x+5)^2)	\frac{dy}{dx}=\frac{4\sec(y)}{(x+5)^{2}}
slope of (-2.8)(-22.8)	slope\:(-2.8)(-22.8)
derivative of 56x^6	\frac{d}{dx}(56x^{6})
derivative of (x^2-3/(x^2-4))	\frac{d}{dx}(\frac{x^{2}-3}{x^{2}-4})
inverse oflaplace [(3+s)/((s+1)^2)]	inverselaplace\:[\frac{3+s}{(s+1)^{2}}]
laplacetransform 1000	laplacetransform\:1000
limit as x approaches 0 of (8^x-10^x)/x	\lim\:_{x\to\:0}(\frac{8^{x}-10^{x}}{x})
derivative of y=(4x)/3	derivative\:y=\frac{4x}{3}
sum from n=1 to infinity of (1/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{n}
(\partial)/(\partial y)(x^3+y^2)	\frac{\partial\:}{\partial\:y}(x^{3}+y^{2})
limit as x approaches 0 of (1+ax)^{a/x}	\lim\:_{x\to\:0}((1+ax)^{\frac{a}{x}})
area x=3-3y^2,x=3y^2-3	area\:x=3-3y^{2},x=3y^{2}-3
integral of (2x)/((x-5)^2)	\int\:\frac{2x}{(x-5)^{2}}dx
derivative of ln(sqrt(4+5x))	\frac{d}{dx}(\ln(\sqrt{4+5x}))

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