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Popular Calculus Problems

integral of (2x+6)^5	\int\:(2x+6)^{5}dx
integral from 2 to infinity of 7/(3x^2)	\int\:_{2}^{\infty\:}\frac{7}{3x^{2}}dx
integral of 1/(x(x^2-36)^{3/2)}	\int\:\frac{1}{x(x^{2}-36)^{\frac{3}{2}}}dx
derivative of 3cos^3(t)	derivative\:3\cos^{3}(t)
(ln(y))^6(dy)/(dx)=x^6y,y(1)=e^2	(\ln(y))^{6}\frac{dy}{dx}=x^{6}y,y(1)=e^{2}
derivative of y=e^x(3-5x+3x^2)	derivative\:y=e^{x}(3-5x+3x^{2})
sum from n=0 to infinity of n^2+1	\sum\:_{n=0}^{\infty\:}n^{2}+1
integral of cos(x)sqrt(4-sin^2(x))	\int\:\cos(x)\sqrt{4-\sin^{2}(x)}dx
integral of x/(sqrt((x^2+1)))	\int\:\frac{x}{\sqrt{(x^{2}+1)}}dx
integral of sqrt(x^9)	\int\:\sqrt{x^{9}}dx
(1-y)e^yy^'+(y^2)/(x*ln(x))=0	(1-y)\cdot\:e^{y}\cdot\:y^{\prime\:}+\frac{y^{2}}{x\cdot\:\ln(x)}=0
integral from 0 to 1/14 of xln(14x)	\int\:_{0}^{\frac{1}{14}}x\ln(14x)dx
derivative of 390-2p-0.1p^2	derivative\:390-2p-0.1p^{2}
integral of x/(sqrt(x^2-7))	\int\:\frac{x}{\sqrt{x^{2}-7}}dx
derivative of 8x+9	\frac{d}{dx}(8x+9)
taylor 3ln(1+2x^2)	taylor\:3\ln(1+2x^{2})
integral of (sqrt(16+x^2))/x	\int\:\frac{\sqrt{16+x^{2}}}{x}dx
integral from 2 to infinity of ye^{-4y}	\int\:_{2}^{\infty\:}ye^{-4y}dy
integral of arcsin(7x)	\int\:\arcsin(7x)dx
derivative of arctan(pi/x)	\frac{d}{dx}(\arctan(\frac{π}{x}))
derivative of 1/(tan(x))	derivative\:\frac{1}{\tan(x)}
(\partial)/(\partial y)(5+xln(xy-7))	\frac{\partial\:}{\partial\:y}(5+x\ln(xy-7))
derivative of x^2+1/(x^2)	derivative\:x^{2}+\frac{1}{x^{2}}
derivative of (x+3ln(4x+2))	\frac{d}{dx}((x+3)\ln(4x+2))
simplify (x^2}{100}+8+\frac{20)/x	simplify\:\frac{x^{2}}{100}+8+\frac{20}{x}
integral of (1.05)/(1+100e^{-0.285x)}	\int\:\frac{1.05}{1+100e^{-0.285x}}dx
sum from n=0 to infinity of 4/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{4}{5^{n}}
integral from 0 to pi/3 of x^2cos(3x)	\int\:_{0}^{\frac{π}{3}}x^{2}\cos(3x)dx
integral of (1/y-2xsin(y))	\int\:(\frac{1}{y}-2x\sin(y))dy
integral of (x+21)/(x^2+20x+104)	\int\:\frac{x+21}{x^{2}+20x+104}dx
(\partial)/(\partial x)(1/(3x^2+2y))	\frac{\partial\:}{\partial\:x}(\frac{1}{3x^{2}+2y})
integral of 7cos(pix)	\int\:7\cos(πx)dx
(\partial)/(\partial x)(x^3y^2(6-x-y))	\frac{\partial\:}{\partial\:x}(x^{3}y^{2}(6-x-y))
derivative of (x-3/(x+5))	\frac{d}{dx}(\frac{x-3}{x+5})
integral of sin^2(1/3 x)	\int\:\sin^{2}(\frac{1}{3}x)dx
inverse oflaplace s/((s^2+5^2)^2)	inverselaplace\:\frac{s}{(s^{2}+5^{2})^{2}}
integral of (sqrt(4+x^2))/x	\int\:\frac{\sqrt{4+x^{2}}}{x}dx
derivative of x/((x-1))	\frac{d}{dx}(\frac{x}{(x-1)})
limit as x approaches 0 of (4e^x-4)/x	\lim\:_{x\to\:0}(\frac{4e^{x}-4}{x})
d/(d{r)}(1/(2sqrt({r))}+1/(3{r)^{2/3}})	\frac{d}{d{r}}(\frac{1}{2\sqrt{{r}}}+\frac{1}{3{r}^{\frac{2}{3}}})
derivative of f(h,x(g(h,x)(h(x))))	\frac{d}{dx}(f(h,x)(g(h,x)(h(x))))
(\partial)/(\partial x)((5x+4y)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{5x+4y}{x+y})
(\partial)/(\partial x)(e^{xyz-8})	\frac{\partial\:}{\partial\:x}(e^{xyz-8})
derivative of (x+1)^2	derivative\:(x+1)^{2}
y^'=(2x+sec^2(x))/(2y),y(0)=-7	y^{\prime\:}=\frac{2x+\sec^{2}(x)}{2y},y(0)=-7
derivative of 2^{(2-x^4})	\frac{d}{dx}(2^{(2-x^{4})})
(dy)/(dx)=(x^3+2y^3)/(xy^2)	\frac{dy}{dx}=\frac{x^{3}+2y^{3}}{xy^{2}}
integral of (((3x-2)^2+(3x+2)^2)/(x^2))	\int\:(\frac{(3x-2)^{2}+(3x+2)^{2}}{x^{2}})dx
derivative of f(x)=(sqrt(x))/(x+2)	derivative\:f(x)=\frac{\sqrt{x}}{x+2}
xy^'+y=-2x^6y^4	xy^{\prime\:}+y=-2x^{6}y^{4}
(\partial)/(\partial x)(y^2sin(x))	\frac{\partial\:}{\partial\:x}(y^{2}\sin(x))
inverse oflaplace e^{-pis} 2/(s^3)	inverselaplace\:e^{-πs}\frac{2}{s^{3}}
y^'-2 y/x =x,y(1)=2	y^{\prime\:}-2\frac{y}{x}=x,y(1)=2
y'=-y^3	y\prime\:=-y^{3}
derivative of y=sin^3(x^2)	derivative\:y=\sin^{3}(x^{2})
sum from n=1 to infinity of (-7/4)^2	\sum\:_{n=1}^{\infty\:}(-\frac{7}{4})^{2}
tangent of (cos(x))/(2+sin(x))	tangent\:\frac{\cos(x)}{2+\sin(x)}
derivative of x^3ln(x+1)	derivative\:x^{3}\ln(x+1)
derivative of 2xcsc(x)-x^2cot(x)csc(x)	derivative\:2x\csc(x)-x^{2}\cot(x)\csc(x)
area-3/8 x(x-8),10-x/2 ,2,8	area\:-\frac{3}{8}x(x-8),10-\frac{x}{2},2,8
derivative of (2x^2+8x+6/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+8x+6}{\sqrt{x}})
integral from 3 to infinity of e^{-x/4}	\int\:_{3}^{\infty\:}e^{-\frac{x}{4}}dx
(\partial)/(\partial x)(9cos(ye^{xy})sin(x))	\frac{\partial\:}{\partial\:x}(9\cos(ye^{xy})\sin(x))
integral of (6x^2+x+3)/((x^2+2)(x-9))	\int\:\frac{6x^{2}+x+3}{(x^{2}+2)(x-9)}dx
(\partial)/(\partial y)(1/x)	\frac{\partial\:}{\partial\:y}(\frac{1}{x})
slope of (1,1),(8,-3/4)	slope\:(1,1),(8,-\frac{3}{4})
derivative of f(x)=(sin(1/x)+cos(1/x))^3	derivative\:f(x)=(\sin(\frac{1}{x})+\cos(\frac{1}{x}))^{3}
limit as h approaches 0 of-5	\lim\:_{h\to\:0}(-5)
limit as x approaches 0 of (e^x-1)/1	\lim\:_{x\to\:0}(\frac{e^{x}-1}{1})
derivative of-y/(x+4y)	derivative\:-\frac{y}{x+4y}
inverse oflaplace 1/((s^2-s-2))	inverselaplace\:\frac{1}{(s^{2}-s-2)}
area x^2-19,18x	area\:x^{2}-19,18x
(\partial)/(\partial x)(1+x*ln(xy-5))	\frac{\partial\:}{\partial\:x}(1+x\cdot\:\ln(xy-5))
y^'+x^2y=x^2	y^{\prime\:}+x^{2}y=x^{2}
derivative of 3(cos(x^2)-2x^2sin(x^2))	derivative\:3(\cos(x^{2})-2x^{2}\sin(x^{2}))
derivative of x^3-2x+3x^{-3}	\frac{d}{dx}(x^{3}-2x+3x^{-3})
derivative of y=ln(log_{e}(3x))	derivative\:y=\ln(\log_{e}(3x))
derivative of-4	derivative\:-4
integral from 1 to infinity of 0	\int\:_{1}^{\infty\:}0dx
integral of sec(x)tan^4(x)	\int\:\sec(x)\tan^{4}(x)dx
integral of x^2-6sqrt(x)	\int\:x^{2}-6\sqrt{x}dx
integral of 1^x	\int\:1^{x}dx
integral of 7e^{cos(x)}sin(x)	\int\:7e^{\cos(x)}\sin(x)dx
laplacetransform cos(2t)-5t	laplacetransform\:\cos(2t)-5t
limit as x approaches 3 of 5x^3-2x^2+x-9	\lim\:_{x\to\:3}(5x^{3}-2x^{2}+x-9)
integral of (tan(2/t))/(t^2)	\int\:\frac{\tan(\frac{2}{t})}{t^{2}}dt
inverse oflaplace 4/(s-3)	inverselaplace\:\frac{4}{s-3}
integral from 3 to 5 of xsqrt(x^2-9)	\int\:_{3}^{5}x\sqrt{x^{2}-9}dx
limit as x approaches infinity of h(x)	\lim\:_{x\to\:\infty\:}(h(x))
integral of 6x(3x^2+5)^3	\int\:6x(3x^{2}+5)^{3}dx
integral of 1/(-x^2-2x)	\int\:\frac{1}{-x^{2}-2x}dx
integral of 1/(4xlog_{3)(x)}	\int\:\frac{1}{4x\log_{3}(x)}dx
(\partial)/(\partial x)(xtan(y))	\frac{\partial\:}{\partial\:x}(x\tan(y))
laplacetransform 3tcos(t)	laplacetransform\:3t\cos(t)
(dx)/(dt)=x+t	\frac{dx}{dt}=x+t
derivative of 1/3 x^3+1/2 x^2	\frac{d}{dx}(\frac{1}{3}x^{3}+\frac{1}{2}x^{2})
tangent of f(x)=2sec(x),\at x= pi/6	tangent\:f(x)=2\sec(x),\at\:x=\frac{π}{6}
derivative of (1/(y^2)-5/(y^4))(y+7y^3)	derivative\:(\frac{1}{y^{2}}-\frac{5}{y^{4}})(y+7y^{3})
(\partial)/(\partial x)((x^αy^β)/(y^{1-α)x^{1-β}})	\frac{\partial\:}{\partial\:x}(\frac{x^{α}y^{β}}{y^{1-α}x^{1-β}})
derivative of (e^x^2)	\frac{d}{dx}((e^{x})^{2})

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