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Popular Calculus Problems

y^'+6x^5y=x^5	y^{\prime\:}+6x^{5}y=x^{5}
y^{''}-y^'=e^tcos(t)	y^{\prime\:\prime\:}-y^{\prime\:}=e^{t}\cos(t)
integral of 1/(e^x-e^{-x)}	\int\:\frac{1}{e^{x}-e^{-x}}dx
integral of sin(xn)	\int\:\sin(xn)dx
(dP)/(dt)=(9P)/(900)(9-P),P(0)=4	\frac{dP}{dt}=\frac{9P}{900}(9-P),P(0)=4
derivative of-12sin(2x)	derivative\:-12\sin(2x)
integral of x^3*sqrt(9-x^2)	\int\:x^{3}\cdot\:\sqrt{9-x^{2}}dx
derivative of ((3x/(x+1))^2)	\frac{d}{dx}((\frac{3x}{x+1})^{2})
derivative of 2sqrt(x^3)	derivative\:2\sqrt{x^{3}}
derivative of e^{xt}	\frac{d}{dx}(e^{xt})
area 3/x ,12x, 1/(12x)	area\:\frac{3}{x},12x,\frac{1}{12x}
integral from 0 to 2 of 8x	\int\:_{0}^{2}8xdx
integral from 2 to 3 of x(x-2)(x+2)	\int\:_{2}^{3}x(x-2)(x+2)dx
tangent of sqrt(x^2-10x+4),(0)	tangent\:\sqrt{x^{2}-10x+4},(0)
integral of 1/(sqrt(x^2-10x+34))	\int\:\frac{1}{\sqrt{x^{2}-10x+34}}dx
sqrt(1-7x^2)y^'=x	\sqrt{1-7x^{2}}y^{\prime\:}=x
limit as x approaches 8+of 1/(x-8)	\lim\:_{x\to\:8+}(\frac{1}{x-8})
(\partial)/(\partial x)(sqrt((16)/(xy)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{16}{xy}})
integral from 0 to 2 of 5/((x-1)^{1/3)}	\int\:_{0}^{2}\frac{5}{(x-1)^{\frac{1}{3}}}dx
limit as x approaches 2 of (x^2+5)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{2}+5}{x-2})
(\partial)/(\partial y)(8xy+8y^2-2x+2y-1)	\frac{\partial\:}{\partial\:y}(8xy+8y^{2}-2x+2y-1)
derivative of (1+5/x ^x)	\frac{d}{dx}((1+\frac{5}{x})^{x})
(\partial)/(\partial z)(xe^{2y+3z})	\frac{\partial\:}{\partial\:z}(xe^{2y+3z})
(\partial)/(\partial x)(ln(x/(2y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{2y}))
integral from 0 to 2/3 of 1/(4+9x^2)	\int\:_{0}^{\frac{2}{3}}\frac{1}{4+9x^{2}}dx
derivative of (e^{x^2}/(cos(3x)))	\frac{d}{dx}(\frac{e^{x^{2}}}{\cos(3x)})
derivative of e^{2x}sin(7x)	\frac{d}{dx}(e^{2x}\sin(7x))
(dy)/(dt)+e^ty=-7e^t	\frac{dy}{dt}+e^{t}y=-7e^{t}
integral of sin^2(1/2 pix)	\int\:\sin^{2}(\frac{1}{2}πx)dx
taylor 5ln(x^2),x=1	taylor\:5\ln(x^{2}),x=1
integral of (9/x)	\int\:(\frac{9}{x})dx
derivative of 2-7x	\frac{d}{dx}(2-7x)
derivative of (sin^2(x)/(sin(x^2)))	\frac{d}{dx}(\frac{\sin^{2}(x)}{\sin(x^{2})})
integral from 0 to pi of sec(x)	\int\:_{0}^{π}\sec(x)dx
integral of sqrt(cos(x))*sin^3(x)	\int\:\sqrt{\cos(x)}\cdot\:\sin^{3}(x)dx
integral from 0 to 1 of (-7y)/(e^{2y)}	\int\:_{0}^{1}\frac{-7y}{e^{2y}}dy
laplacetransform e^{-10t}	laplacetransform\:e^{-10t}
integral from 0 to pi of cos^2(x)sin(x)	\int\:_{0}^{π}\cos^{2}(x)\sin(x)dx
derivative of 2cos^3(x)	derivative\:2\cos^{3}(x)
integral of (sqrt(8x)-2x)	\int\:(\sqrt{8x}-2x)dx
integral of 1/(1+2sin(x))	\int\:\frac{1}{1+2\sin(x)}dx
(dy)/(dx)=y+6	\frac{dy}{dx}=y+6
integral of 12xsqrt(1+6x^2)	\int\:12x\sqrt{1+6x^{2}}dx
y^'=12xy-2x	y^{\prime\:}=12xy-2x
(\partial)/(\partial x)(2ye^{5x^2-6y})	\frac{\partial\:}{\partial\:x}(2ye^{5x^{2}-6y})
integral from-1 to 1 of xe^{x+1}	\int\:_{-1}^{1}xe^{x+1}dx
limit as x approaches 0 of 9x-4	\lim\:_{x\to\:0}(9x-4)
integral of 1/(16+25x^2)+2/(3(x-2))	\int\:\frac{1}{16+25x^{2}}+\frac{2}{3(x-2)}dx
limit as x approaches pi of-9sin(x/2)	\lim\:_{x\to\:π}(-9\sin(\frac{x}{2}))
derivative of f(x)=(-9x^2+16)^2	derivative\:f(x)=(-9x^{2}+16)^{2}
integral of sqrt(6x)	\int\:\sqrt{6x}dx
integral of (x+1)/(x^2-4x+3)	\int\:\frac{x+1}{x^{2}-4x+3}dx
area y=x^2-2,y=7	area\:y=x^{2}-2,y=7
tangent of f(x)=(-6x)/(x^2+1),(0,0)	tangent\:f(x)=\frac{-6x}{x^{2}+1},(0,0)
tangent of x^2+4	tangent\:x^{2}+4
integral of 1/(sin(y/2))	\int\:\frac{1}{\sin(\frac{y}{2})}dy
integral from 0 to t of 1/(1+r)	\int\:_{0}^{t}\frac{1}{1+r}dr
integral of-4x-8	\int\:-4x-8dx
sum from n=1 to infinity of 5e^{-6n}	\sum\:_{n=1}^{\infty\:}5e^{-6n}
integral from 0 to 1 of 3(1+sqrt(x))^8	\int\:_{0}^{1}3(1+\sqrt{x})^{8}dx
integral of csc^4(5x)cot^4(5x)	\int\:\csc^{4}(5x)\cot^{4}(5x)dx
derivative of 2xe^{-x^2}	\frac{d}{dx}(2xe^{-x^{2}})
(y^{16})dy=((1+x))/x dx,y(1)=5	(y^{16})dy=\frac{(1+x)}{x}dx,y(1)=5
inverse oflaplace ((s^2+s))/(2s^2+2s+1)	inverselaplace\:\frac{(s^{2}+s)}{2s^{2}+2s+1}
derivative of f(x)= 1/((3x+8)^2)	derivative\:f(x)=\frac{1}{(3x+8)^{2}}
derivative of (-x^2+2x+1/((x^2+1)^2))	\frac{d}{dx}(\frac{-x^{2}+2x+1}{(x^{2}+1)^{2}})
integral of cos(2pinx)	\int\:\cos(2πnx)dx
sum from n=0 to infinity of ((x-3)^n)/n	\sum\:_{n=0}^{\infty\:}\frac{(x-3)^{n}}{n}
derivative of 1/(e^{1/x})	\frac{d}{dx}(\frac{1}{e^{\frac{1}{x}}})
derivative of 2x-9	\frac{d}{dx}(2x-9)
limit as x approaches 0 of 4^x	\lim\:_{x\to\:0}(4^{x})
inverse oflaplace (s-5)/((s^2-6s+25))	inverselaplace\:\frac{s-5}{(s^{2}-6s+25)}
tangent of x^4-4x^3-2,\at x=1	tangent\:x^{4}-4x^{3}-2,\at\:x=1
derivative of f(x)=2xe^{4x}	derivative\:f(x)=2xe^{4x}
sum from n=0 to infinity of (n(n+1))/2	\sum\:_{n=0}^{\infty\:}\frac{n(n+1)}{2}
limit as x approaches-1-of (x-1)/(x+1)	\lim\:_{x\to\:-1-}(\frac{x-1}{x+1})
integral from 0 to 1/2 of cos(pix)	\int\:_{0}^{\frac{1}{2}}\cos(πx)dx
(2xy+3y^2)dx-(x^2+2xy)dy=0	(2xy+3y^{2})dx-(x^{2}+2xy)dy=0
tangent of f(x)=34x-16x^2,\at x=1	tangent\:f(x)=34x-16x^{2},\at\:x=1
derivative of 10e^{10x}	derivative\:10e^{10x}
(\partial)/(\partial m)((G(m,r)m)/(r^2))	\frac{\partial\:}{\partial\:m}(\frac{G(m,r)m}{r^{2}})
limit as x approaches 0-of x*e^{1/x}	\lim\:_{x\to\:0-}(x\cdot\:e^{\frac{1}{x}})
derivative of (1-6t)/(4+t)	derivative\:\frac{1-6t}{4+t}
derivative of 4cot(x/8)	\frac{d}{dx}(4\cot(\frac{x}{8}))
inverse oflaplace 0.5	inverselaplace\:0.5
integral of (x^6+1/(sqrt(1-4x^2)))	\int\:(x^{6}+\frac{1}{\sqrt{1-4x^{2}}})dx
integral from 8 to infinity of 1/(x^2+x)	\int\:_{8}^{\infty\:}\frac{1}{x^{2}+x}dx
y^'=(y+4x)^2	y^{\prime\:}=(y+4x)^{2}
limit as x approaches 1+of (x^2)/(x^2-1)	\lim\:_{x\to\:1+}(\frac{x^{2}}{x^{2}-1})
(dy)/(dx)=3e^{2x}y^2	\frac{dy}{dx}=3e^{2x}y^{2}
taylor ln(x+2)	taylor\:\ln(x+2)
integral of x^35^{-x}	\int\:x^{3}5^{-x}dx
integral of (x^2+2x-1)cos(3x)	\int\:(x^{2}+2x-1)\cos(3x)dx
integral from 0 to 1 of e^{(2x)/3}	\int\:_{0}^{1}e^{\frac{2x}{3}}dx
(dy)/(dx)=((x+sin(x)))/(3y^2)	\frac{dy}{dx}=\frac{(x+\sin(x))}{3y^{2}}
derivative of x^3-2x^2+4x+3	derivative\:x^{3}-2x^{2}+4x+3
derivative of sin((pix^7))	\frac{d}{dx}(\sin((πx)^{7}))
(\partial)/(\partial x)(ln(x^2+y^4+2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{4}+2))
sum from n=1 to infinity of n/(n^2+2)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+2}
derivative of-8sin((3x/2+1))	\frac{d}{dx}(-8\sin(\frac{3x}{2}+1))

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