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Popular Calculus Problems

y^{''}-2y^'+3y=6sin(3x)-6cos(3x)	y^{\prime\:\prime\:}-2y^{\prime\:}+3y=6\sin(3x)-6\cos(3x)
(10+x^2)y^'-2xy=0	(10+x^{2})y^{\prime\:}-2xy=0
integral of x^2-3x+7	\int\:x^{2}-3x+7dx
derivative of 2/3 x^6	derivative\:\frac{2}{3}x^{6}
integral from 7 to 8 of 1/((x-7)^{3/2)}	\int\:_{7}^{8}\frac{1}{(x-7)^{\frac{3}{2}}}dx
(x+1)((dy)/(dx))=(x+6)	(x+1)(\frac{dy}{dx})=(x+6)
limit as x approaches 0 of x^{-8}	\lim\:_{x\to\:0}(x^{-8})
integral of sin(5x-1)	\int\:\sin(5x-1)dx
integral of (x+7)/((x+2)(x-3))	\int\:\frac{x+7}{(x+2)(x-3)}dx
integral of q	\int\:qdq
derivative of h(t)=((t^3)/(t^8+9))^2	derivative\:h(t)=(\frac{t^{3}}{t^{8}+9})^{2}
derivative of sin(x+cos(x))	\frac{d}{dx}(\sin(x)+\cos(x))
integral of ((cos^5(x)))/(sqrt(sin(x)))	\int\:\frac{(\cos^{5}(x))}{\sqrt{\sin(x)}}dx
integral of 6x^2-5x-1	\int\:6x^{2}-5x-1dx
derivative of f(x)=(3x-4)^2	derivative\:f(x)=(3x-4)^{2}
y^{''}+2y^'=2x+3-e^{-2x}	y^{\prime\:\prime\:}+2y^{\prime\:}=2x+3-e^{-2x}
(dr)/(dθ)+rtan(θ)=5sec(θ)	\frac{dr}{dθ}+r\tan(θ)=5\sec(θ)
integral of (1/2)/(sqrt(4-3x^2))	\int\:\frac{\frac{1}{2}}{\sqrt{4-3x^{2}}}dx
integral of arcsec(y)	\int\:\arcsec(y)dy
integral of sec^2(θ)tan^6(θ)	\int\:\sec^{2}(θ)\tan^{6}(θ)dθ
derivative of e^p(p+psqrt(p))	derivative\:e^{p}(p+p\sqrt{p})
(\partial)/(\partial x)(y/(1+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{1+x^{2}y^{2}})
y^'-a*y+b=0	y^{\prime\:}-a\cdot\:y+b=0
y^'=((e^{(x/3)}+y))/2	y^{\prime\:}=\frac{(e^{(\frac{x}{3})}+y)}{2}
derivative of-4sin(8x)	\frac{d}{dx}(-4\sin(8x))
limit as x approaches 0 of x/(1+x)	\lim\:_{x\to\:0}(\frac{x}{1+x})
area x^2-6,3	area\:x^{2}-6,3
derivative of f(x)=-2x^4+x^{-2}-3x^{3/4}	derivative\:f(x)=-2x^{4}+x^{-2}-3x^{\frac{3}{4}}
taylor cos(pi-7x)	taylor\:\cos(π-7x)
integral from 0 to 3 of x^{1/2}	\int\:_{0}^{3}x^{\frac{1}{2}}dx
derivative of 1/(x^{23/9)}	derivative\:\frac{1}{x^{\frac{23}{9}}}
integral from 1 to infinity of x^{-1/6}	\int\:_{1}^{\infty\:}x^{-\frac{1}{6}}dx
limit as x approaches 8-of 7/(x-8)	\lim\:_{x\to\:8-}(\frac{7}{x-8})
derivative of-24e^{-8x^3}x^2	\frac{d}{dx}(-24e^{-8x^{3}}x^{2})
derivative of x^2-2sqrt(x)	\frac{d}{dx}(x^{2}-2\sqrt{x})
derivative of cos(x+x*sin(x))	\frac{d}{dx}(\cos(x)+x\cdot\:\sin(x))
derivative of f(x)=(x^3+8)e^x	derivative\:f(x)=(x^{3}+8)e^{x}
slope of y=(16)/((x+4)^2),(0,1)	slope\:y=\frac{16}{(x+4)^{2}},(0,1)
integral of q/k r^2	\int\:\frac{q}{k}r^{2}dr
limit as x approaches 2 of 1/(sqrt(3.9))	\lim\:_{x\to\:2}(\frac{1}{\sqrt{3.9}})
area y=tan(x),y=-3tan(x),x= pi/4	area\:y=\tan(x),y=-3\tan(x),x=\frac{π}{4}
derivative of 3sin(x^2)	\frac{d}{dx}(3\sin(x^{2}))
limit as x approaches 0 of (9^x-13^x)/x	\lim\:_{x\to\:0}(\frac{9^{x}-13^{x}}{x})
tangent of (8x-x^2)(1.7)	tangent\:(8x-x^{2})(1.7)
derivative of (x^3+2x+6(4+1/(x^2)))	\frac{d}{dx}((x^{3}+2x+6)(4+\frac{1}{x^{2}}))
integral from 0 to infinity of e^{-5x}	\int\:_{0}^{\infty\:}e^{-5x}dx
integral of (-x-1)/x	\int\:\frac{-x-1}{x}dx
derivative of (1+e^{-t})^{-1}+e^{-1}	derivative\:(1+e^{-t})^{-1}+e^{-1}
integral of 5v(v^2+2)^2	\int\:5v(v^{2}+2)^{2}dv
(dy)/(dx)y=(sec(x))/(1+sec(x))	\frac{dy}{dx}y=\frac{\sec(x)}{1+\sec(x)}
integral from 0 to 1 of x/((2x+1)^3)	\int\:_{0}^{1}\frac{x}{(2x+1)^{3}}dx
integral of 1/(x^{8/9)(8+x^{1/9})}	\int\:\frac{1}{x^{\frac{8}{9}}(8+x^{\frac{1}{9}})}dx
integral of 4x^2sec(5x^3)	\int\:4x^{2}\sec(5x^{3})dx
integral from 0 to pi/4 of 3tan^3(x)	\int\:_{0}^{\frac{π}{4}}3\tan^{3}(x)dx
derivative of 4arccot(x/2)	\frac{d}{dx}(4\arccot(\frac{x}{2}))
integral of (2x-1)/(x^2-6x+18)	\int\:\frac{2x-1}{x^{2}-6x+18}dx
(\partial)/(\partial z)(e^{3x+4y}cos(5z))	\frac{\partial\:}{\partial\:z}(e^{3x+4y}\cos(5z))
integral of (1+1/t)^3(1/(t^2))	\int\:(1+\frac{1}{t})^{3}(\frac{1}{t^{2}})dt
sum from n=1 to infinity of (0.1)^n	\sum\:_{n=1}^{\infty\:}(0.1)^{n}
derivative of (2x+5/(x^2-3))	\frac{d}{dx}(\frac{2x+5}{x^{2}-3})
derivative of f(x)=-3x+4	derivative\:f(x)=-3x+4
slope of (0,0),(3,4)	slope\:(0,0),(3,4)
derivative of-3/(4s^4)+(10)/(3s^3)	derivative\:-\frac{3}{4s^{4}}+\frac{10}{3s^{3}}
limit as x approaches-1 of ((x-2))/(x+1)	\lim\:_{x\to\:-1}(\frac{(x-2)}{x+1})
xy^'=y+x,y(1)=1	xy^{\prime\:}=y+x,y(1)=1
laplacetransform 10ln(0.5)x	laplacetransform\:10\ln(0.5)x
integral of x^3cos(4x)	\int\:x^{3}\cos(4x)dx
derivative of a	derivative\:a
(y^2+8)dx=ysec^2(x)dy	(y^{2}+8)dx=y\sec^{2}(x)dy
integral of 3(3x-1)^4	\int\:3(3x-1)^{4}dx
limit as x approaches 1 of e^{3x^5-3x}	\lim\:_{x\to\:1}(e^{3x^{5}-3x})
derivative of f(x)= 5/x	derivative\:f(x)=\frac{5}{x}
integral of 3sqrt(x)-2\sqrt[3]{x}	\int\:3\sqrt{x}-2\sqrt[3]{x}dx
limit as n approaches infinity of sin((npi)/4)	\lim\:_{n\to\:\infty\:}(\sin(\frac{nπ}{4}))
derivative of e^{1/x}-(e^{1/x})/x	derivative\:e^{\frac{1}{x}}-\frac{e^{\frac{1}{x}}}{x}
derivative of sqrt(x)sec(x+3)	\frac{d}{dx}(\sqrt{x}\sec(x)+3)
integral of (2x)/(2x+1)	\int\:\frac{2x}{2x+1}dx
(\partial)/(\partial x)((cos(y))/(xz^2))	\frac{\partial\:}{\partial\:x}(\frac{\cos(y)}{xz^{2}})
integral of 1/((3+2x)^2)	\int\:\frac{1}{(3+2x)^{2}}dx
integral from 0 to 2 of 4ti-t^3j+4t^7k	\int\:_{0}^{2}4ti-t^{3}j+4t^{7}kdt
derivative of-x/(x-1)	\frac{d}{dx}(-\frac{x}{x-1})
limit as x approaches 0 of (9cos(x)-9)/x	\lim\:_{x\to\:0}(\frac{9\cos(x)-9}{x})
derivative of (x-6/(3x-2))	\frac{d}{dx}(\frac{x-6}{3x-2})
derivative of y=(x^5+2)^2(x^3+4)^4	derivative\:y=(x^{5}+2)^{2}(x^{3}+4)^{4}
derivative of 1/2 ln(x^2+y^2)	\frac{d}{dx}(\frac{1}{2}\ln(x^{2}+y^{2}))
(d^2)/(dx^2)(1/((x-1)^2))	\frac{d^{2}}{dx^{2}}(\frac{1}{(x-1)^{2}})
integral of x^2e^{20x}	\int\:x^{2}e^{20x}dx
sum from n=0 to infinity of (x-5)^n	\sum\:_{n=0}^{\infty\:}(x-5)^{n}
derivative of f(x)=2pix	derivative\:f(x)=2πx
tangent of f(x)=sqrt(x+7),\at x=2	tangent\:f(x)=\sqrt{x+7},\at\:x=2
derivative of (7x-11/(sqrt(x)))	\frac{d}{dx}(\frac{7x-11}{\sqrt{x}})
y^'=9xe^y,y(0)=0	y^{\prime\:}=9xe^{y},y(0)=0
area 7-2x^2,x^2+4	area\:7-2x^{2},x^{2}+4
limit as t approaches 0 of sin(2t)	\lim\:_{t\to\:0}(\sin(2t))
integral of 1/(x^3sqrt(x^2-9))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-9}}dx
derivative of xlog_{e}(x)	\frac{d}{dx}(x\log_{e}(x))
(\partial)/(\partial x)(7xy^9+x^5y^7)	\frac{\partial\:}{\partial\:x}(7xy^{9}+x^{5}y^{7})
derivative of 2x+4/x	\frac{d}{dx}(2x+\frac{4}{x})
integral of (18)/(1-cos(2x))	\int\:\frac{18}{1-\cos(2x)}dx
integral of (5x^4)/((10+x^5)^4)	\int\:\frac{5x^{4}}{(10+x^{5})^{4}}dx

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