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Popular Calculus Problems

integral of 8t^5	\int\:8t^{5}dt
derivative of axcos(x+bxsin(x))	\frac{d}{dx}(ax\cos(x)+bx\sin(x))
limit as x approaches 6+of sqrt(6-x)	\lim\:_{x\to\:6+}(\sqrt{6-x})
derivative of 4x^2sin(x)tan(x)	derivative\:4x^{2}\sin(x)\tan(x)
integral of (3x)/(sqrt(4x^2+5))	\int\:\frac{3x}{\sqrt{4x^{2}+5}}dx
derivative of sqrt(7-2x)	\frac{d}{dx}(\sqrt{7-2x})
integral from 1 to e of x^2ln(x)	\int\:_{1}^{e}x^{2}\ln(x)dx
limit as x approaches 0 of (3x)/(tan(x))	\lim\:_{x\to\:0}(\frac{3x}{\tan(x)})
y^'-2xy=2x	y^{\prime\:}-2xy=2x
limit as x approaches 1 of arctan(x)	\lim\:_{x\to\:1}(\arctan(x))
y^'-4/x y= 1/(x^3)y^4	y^{\prime\:}-\frac{4}{x}y=\frac{1}{x^{3}}y^{4}
derivative of-30sin(x)	\frac{d}{dx}(-30\sin(x))
integral of x/(sqrt(x^2+x+2))	\int\:\frac{x}{\sqrt{x^{2}+x+2}}dx
integral of 7t	\int\:7tdt
integral of sin(7pit)	\int\:\sin(7πt)dt
derivative of csc(x+cot(x))	\frac{d}{dx}(\csc(x)+\cot(x))
laplacetransform e^{-t}sin(3t)	laplacetransform\:e^{-t}\sin(3t)
derivative of cos(x-x^2(1-2x))	\frac{d}{dx}(\cos(x-x^{2})(1-2x))
limit as x approaches 0 of 1/x ln(1-2x)	\lim\:_{x\to\:0}(\frac{1}{x}\ln(1-2x))
derivative of (2x+3x^2/(x^2e^x))	\frac{d}{dx}(\frac{2x+3x^{2}}{x^{2}e^{x}})
laplacetransform te^{-3t}cos(3t)	laplacetransform\:te^{-3t}\cos(3t)
derivative of (80-x/4)	\frac{d}{dx}(\frac{80-x}{4})
integral of xsin^2(2x)	\int\:x\sin^{2}(2x)dx
derivative of 4t^3	derivative\:4t^{3}
derivative of [x+(x+sin^2(x))^3]^6	derivative\:[x+(x+\sin^{2}(x))^{3}]^{6}
integral of (ln(x))/(x(1-ln^2(x)))	\int\:\frac{\ln(x)}{x(1-\ln^{2}(x))}dx
integral from 0 to pi/2 of-9sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-9\sin^{2}(3x)dx
laplacetransform 7cos(3t)	laplacetransform\:7\cos(3t)
d/(ds)(s/(s^2+w^2))	\frac{d}{ds}(\frac{s}{s^{2}+w^{2}})
derivative of-8e^{-3x}	\frac{d}{dx}(-8e^{-3x})
sum from n=0 to infinity of 2/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{2}{5^{n}}
derivative of sqrt(csc(2x))	\frac{d}{dx}(\sqrt{\csc(2x)})
(dy)/(dx)=-(sqrt(x))/(4y)	\frac{dy}{dx}=-\frac{\sqrt{x}}{4y}
derivative of cos(x-pi/6)	\frac{d}{dx}(\cos(x-\frac{π}{6}))
derivative of y=(1-5x)^6	derivative\:y=(1-5x)^{6}
integral of 5/(36+x^2)	\int\:\frac{5}{36+x^{2}}dx
integral from-1 to 4 of (7y)/(y^2-3y-10)	\int\:_{-1}^{4}\frac{7y}{y^{2}-3y-10}dy
limit as x approaches pi/2+of sin(x)	\lim\:_{x\to\:\frac{π}{2}+}(\sin(x))
derivative of (3x^2-9^{-14})	\frac{d}{dx}((3x^{2}-9)^{-14})
integral of 1/(sqrt(x))cos^2(sqrt(x))	\int\:\frac{1}{\sqrt{x}}\cos^{2}(\sqrt{x})dx
integral from 0 to a of 7x^2sqrt(a^2-x^2)	\int\:_{0}^{a}7x^{2}\sqrt{a^{2}-x^{2}}dx
derivative of sqrt(4x^2-8x)	\frac{d}{dx}(\sqrt{4x^{2}-8x})
limit as x approaches 16 of (sqrt(x-4))/(\sqrt[4]{x-2)}	\lim\:_{x\to\:16}(\frac{\sqrt{x-4}}{\sqrt[4]{x-2}})
limit as x approaches infinity of e^{-3x}sin(x)	\lim\:_{x\to\:\infty\:}(e^{-3x}\sin(x))
derivative of-4sin(x)-9ln(x)+11	derivative\:-4\sin(x)-9\ln(x)+11
derivative of f(x)=cos((x+1)/(x-1))	derivative\:f(x)=\cos(\frac{x+1}{x-1})
integral of (30)/((x-1)(x^2+9))	\int\:\frac{30}{(x-1)(x^{2}+9)}dx
integral of cos(6t)	\int\:\cos(6t)dt
area 4sqrt(2x),2x^2,-4x+6	area\:4\sqrt{2x},2x^{2},-4x+6
(\partial)/(\partial l)(2pisqrt(l/({g))})	\frac{\partial\:}{\partial\:l}(2π\sqrt{\frac{l}{{g}}})
derivative of ln(sqrt((x^2-1/(x^2+1))))	\frac{d}{dx}(\ln(\sqrt{\frac{x^{2}-1}{x^{2}+1}}))
integral from 0 to 1 of 7e^x-7xe^{x^2}	\int\:_{0}^{1}7e^{x}-7xe^{x^{2}}dx
derivative of sin(pi/2 x)	\frac{d}{dx}(\sin(\frac{π}{2}x))
integral from 0 to 6 of (7t)/((t-7)^2)	\int\:_{0}^{6}\frac{7t}{(t-7)^{2}}dt
integral of cos(4x)cos(8x)	\int\:\cos(4x)\cos(8x)dx
y^{''}-4y^'-12y=8e^{-2x}	y^{\prime\:\prime\:}-4y^{\prime\:}-12y=8e^{-2x}
derivative of xe^xcos(x)	\frac{d}{dx}(xe^{x}\cos(x))
integral of (5x^2+2x^3)	\int\:(5x^{2}+2x^{3})dx
integral of (3x+5)^6	\int\:(3x+5)^{6}dx
(\partial)/(\partial x)(5cos(5x))	\frac{\partial\:}{\partial\:x}(5\cos(5x))
integral of t+1	\int\:t+1dt
implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10	implicit\:\frac{dy}{dx},x^{(\frac{2}{3})}+y^{(\frac{2}{3})}=10
derivative of Y(θ)=cot^2(cos(θ))	derivative\:Y(θ)=\cot^{2}(\cos(θ))
derivative of f(t)=6t-5t^2	derivative\:f(t)=6t-5t^{2}
derivative of (x^3+6e^x)	\frac{d}{dx}((x^{3}+6)e^{x})
derivative of sinh(0)	\frac{d}{dx}(\sinh(0))
(dv)/(dt)= 1/(t^2)	\frac{dv}{dt}=\frac{1}{t^{2}}
tangent of 3-2cos(x),\at x= pi/2	tangent\:3-2\cos(x),\at\:x=\frac{π}{2}
integral of 8/(8+e^x)	\int\:\frac{8}{8+e^{x}}dx
slope of y^2=9x,\at x=16	slope\:y^{2}=9x,\at\:x=16
limit as x approaches-3 of sqrt(4x+28-4)	\lim\:_{x\to\:-3}(\sqrt{4x+28-4})
derivative of (7sqrt(x)/(2x^3))	\frac{d}{dx}(\frac{7\sqrt{x}}{2x^{3}})
f(x)=1-\sqrt[3]{x^2}	f(x)=1-\sqrt[3]{x^{2}}
integral of (2x+5)^2	\int\:(2x+5)^{2}dx
integral of (5x^2+7)/(x^{4/3)}	\int\:\frac{5x^{2}+7}{x^{\frac{4}{3}}}dx
(\partial)/(\partial x)((2x^3-4y)(2x^2-4))	\frac{\partial\:}{\partial\:x}((2x^{3}-4y)(2x^{2}-4))
derivative of cos(pi/2)	\frac{d}{dx}(\cos(\frac{π}{2}))
integral of 1/(x^2-2x+8)	\int\:\frac{1}{x^{2}-2x+8}dx
integral of (tan(x))^3(sec(x))^2	\int\:(\tan(x))^{3}(\sec(x))^{2}dx
derivative of 1/(x^4)	derivative\:\frac{1}{x^{4}}
derivative of x^4+5x^{-1}	\frac{d}{dx}(x^{4}+5x^{-1})
derivative of e^{2sin(3x})	\frac{d}{dx}(e^{2\sin(3x)})
f(x)=(sin(x)-cos(x))/(sin(x)+cos(x))	f(x)=\frac{\sin(x)-\cos(x)}{\sin(x)+\cos(x)}
derivative of t^3-12t^2+36t	derivative\:t^{3}-12t^{2}+36t
derivative of 18cos(x)+9sin^2(x)	derivative\:18\cos(x)+9\sin^{2}(x)
(d^2y)/(dx^2)-5(dy)/(dx)+6y=0	\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0
(dy}{dx}=\frac{x^2)/9+7/9	\frac{dy}{dx}=\frac{x^{2}}{9}+\frac{7}{9}
derivative of (cos(x)^2-2sin(x))	\frac{d}{dx}((\cos(x))^{2}-2\sin(x))
limit as x approaches infinity of (ln(x^5))/(13x)	\lim\:_{x\to\:\infty\:}(\frac{\ln(x^{5})}{13x})
integral of pi(2x)^2	\int\:π(2x)^{2}dx
derivative of 4cos(x+4sin(x))	\frac{d}{dx}(4\cos(x)+4\sin(x))
derivative of 2xsin(x)+cos(x)x^2	derivative\:2x\sin(x)+\cos(x)x^{2}
integral of 4e^{-4x}	\int\:4e^{-4x}dx
integral from 0 to (5pi)/4 of 3tan(x/5)	\int\:_{0}^{\frac{5π}{4}}3\tan(\frac{x}{5})dx
implicit (dy)/(dx),y=7^x	implicit\:\frac{dy}{dx},y=7^{x}
derivative of y=(0.9e^x)/(tan(x))	derivative\:y=\frac{0.9e^{x}}{\tan(x)}
f(x)=-4sin(2x)+3cos(3x)	f(x)=-4\sin(2x)+3\cos(3x)
integral of (x^3-4x^2-4x+20)/(x^2-5)	\int\:\frac{x^{3}-4x^{2}-4x+20}{x^{2}-5}dx
derivative of f(x)=8e^{-x}+e^{3x}	derivative\:f(x)=8e^{-x}+e^{3x}
inverse oflaplace (s+1)/(s^2)	inverselaplace\:\frac{s+1}{s^{2}}

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