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Popular Calculus Problems

derivative of (sqrt(x)^4)	\frac{d}{dx}((\sqrt{x})^{4})
integral of (t^2)/(\sqrt[3]{t^3+8)}	\int\:\frac{t^{2}}{\sqrt[3]{t^{3}+8}}dt
integral of (sec^2(1/(x^3)))/(x^4)	\int\:\frac{\sec^{2}(\frac{1}{x^{3}})}{x^{4}}dx
integral of (cos(pi/(x^{19)}))/(x^{20)}	\int\:\frac{\cos(\frac{π}{x^{19}})}{x^{20}}dx
(dy)/(dx)= 1/x (y^2+0.8y)	\frac{dy}{dx}=\frac{1}{x}(y^{2}+0.8y)
integral of (\|x\|)	\int\:(\left\|x\right\|)dx
derivative of 4x^2+3	\frac{d}{dx}(4x^{2}+3)
integral of xsqrt(4+x^2)	\int\:x\sqrt{4+x^{2}}dx
tangent of x+4/x	tangent\:x+\frac{4}{x}
d/(dy)((y^4)/4+1/(8y^2))	\frac{d}{dy}(\frac{y^{4}}{4}+\frac{1}{8y^{2}})
(d^2)/(dx^2)(xsqrt(x^2+1))	\frac{d^{2}}{dx^{2}}(x\sqrt{x^{2}+1})
integral of 2x^{1/4}-3x^3	\int\:2x^{\frac{1}{4}}-3x^{3}dx
d/(dθ)(14sin(θ))	\frac{d}{dθ}(14\sin(θ))
(dy)/(dx)=2xe^{-y}	\frac{dy}{dx}=2xe^{-y}
integral of 1/(sqrt(a-by))	\int\:\frac{1}{\sqrt{a-by}}dy
y^'=y(7-y)-49/4 ,y(0)=a	y^{\prime\:}=y(7-y)-\frac{49}{4},y(0)=a
y^'=((3x^4+y^4))/(xy^3)	y^{\prime\:}=\frac{(3x^{4}+y^{4})}{xy^{3}}
derivative of x^3-cos(x)	\frac{d}{dx}(x^{3}-\cos(x))
integral of-7sin(x)	\int\:-7\sin(x)dx
derivative of-7/(x^3)	derivative\:-\frac{7}{x^{3}}
ydy= 2/x dx	ydy=\frac{2}{x}dx
(2x+2x^{-2}y)dx+(xy-x^{-1})dy=0	(2x+2x^{-2}y)dx+(xy-x^{-1})dy=0
(\partial)/(\partial y)(sqrt(6x-3y))	\frac{\partial\:}{\partial\:y}(\sqrt{6x-3y})
derivative of sinh(4x)	\frac{d}{dx}(\sinh(4x))
integral of cosh(2x)	\int\:\cosh(2x)dx
limit as x approaches 0 of x/(x^2-2)	\lim\:_{x\to\:0}(\frac{x}{x^{2}-2})
limit as x approaches 2 of (x^2+x)/(x+3)	\lim\:_{x\to\:2}(\frac{x^{2}+x}{x+3})
limit as x approaches 1 of r(t)	\lim\:_{x\to\:1}(r(t))
derivative of (x^2)/(ln(3^x))	derivative\:\frac{x^{2}}{\ln(3^{x})}
integral of xln(10x)	\int\:x\ln(10x)dx
integral of sec(x)tan(x)-2e^x	\int\:\sec(x)\tan(x)-2e^{x}dx
integral of sin^5(2θ)	\int\:\sin^{5}(2θ)dθ
(\partial)/(\partial x)(5x^2y)	\frac{\partial\:}{\partial\:x}(5x^{2}y)
integral of 9cos^4(x)	\int\:9\cos^{4}(x)dx
slope ofintercept (2,4),(3,6)	slopeintercept\:(2,4),(3,6)
integral of x/((x^2-2)^2)	\int\:\frac{x}{(x^{2}-2)^{2}}dx
derivative of y=e^{1-x}	derivative\:y=e^{1-x}
derivative of ln^2(3x)	\frac{d}{dx}(\ln^{2}(3x))
inverse oflaplace F(s)=(2/s-1/(s^3))^2	inverselaplace\:F(s)=(\frac{2}{s}-\frac{1}{s^{3}})^{2}
integral of (1+2x^2)e^{x^2}	\int\:(1+2x^{2})e^{x^{2}}dx
limit as x approaches 3 of xsqrt(13-x^2)	\lim\:_{x\to\:3}(x\sqrt{13-x^{2}})
integral from 1 to 2 of sqrt(x)	\int\:_{1}^{2}\sqrt{x}dx
inverse oflaplace (5e^{-2s})/(s^2+4)	inverselaplace\:\frac{5e^{-2s}}{s^{2}+4}
integral of (2x^3+1)^7x^2	\int\:(2x^{3}+1)^{7}x^{2}dx
(\partial)/(\partial y)(Tx^5y^4z^8)	\frac{\partial\:}{\partial\:y}(Tx^{5}y^{4}z^{8})
area (x^2)/(x^3-3x), 1/(x^3-3x),2,11	area\:\frac{x^{2}}{x^{3}-3x},\frac{1}{x^{3}-3x},2,11
derivative of (xe^x/(sin(x)+1))	\frac{d}{dx}(\frac{xe^{x}}{\sin(x)+1})
derivative of tan^2(3x)	derivative\:\tan^{2}(3x)
derivative of y=6x^3ln(5x)	derivative\:y=6x^{3}\ln(5x)
taylor (sqrt(x))/2 ,4	taylor\:\frac{\sqrt{x}}{2},4
(\partial)/(\partial x)(yze^{xz}+30)	\frac{\partial\:}{\partial\:x}(yze^{xz}+30)
derivative of cos^2(x^7)	\frac{d}{dx}(\cos^{2}(x^{7}))
integral of sin(8x)sin(3x)	\int\:\sin(8x)\sin(3x)dx
limit as x approaches 1-of 4-x^2	\lim\:_{x\to\:1-}(4-x^{2})
derivative of (150x/(x+1))	\frac{d}{dx}(\frac{150x}{x+1})
integral of (33x)/(x^2+8x+7)	\int\:\frac{33x}{x^{2}+8x+7}dx
integral of 8x^2\sqrt[4]{4+4x^3}	\int\:8x^{2}\sqrt[4]{4+4x^{3}}dx
integral of ((e^{2y}-y))/(e^y)	\int\:\frac{(e^{2y}-y)}{e^{y}}dy
inverse oflaplace 1/(s^2(s^2+4))	inverselaplace\:\frac{1}{s^{2}(s^{2}+4)}
derivative of (x^2-12)(2x-9)	derivative\:(x^{2}-12)(2x-9)
integral from x to 2 of 0.5	\int\:_{x}^{2}0.5dy
integral of (sin(x))^5	\int\:(\sin(x))^{5}dx
integral of x^2*e^{5x}	\int\:x^{2}\cdot\:e^{5x}dx
sum from n=-1 to infinity of (1/2)^n	\sum\:_{n=-1}^{\infty\:}(\frac{1}{2})^{n}
integral from-infinity to 0 of 1/(7-10x)	\int\:_{-\infty\:}^{0}\frac{1}{7-10x}dx
derivative of 2x^2+3x-5	\frac{d}{dx}(2x^{2}+3x-5)
integral of (x^3)/3 (1/x)	\int\:\frac{x^{3}}{3}(\frac{1}{x})dx
integral of (2x^5)/(3x^2+4)	\int\:\frac{2x^{5}}{3x^{2}+4}dx
derivative of sin(-1x)	\frac{d}{dx}(\sin(-1x))
integral of 3x^2+6x	\int\:3x^{2}+6xdx
derivative of 100e^{-2x}	\frac{d}{dx}(100e^{-2x})
derivative of sqrt((x^3/(2-x)))	\frac{d}{dx}(\sqrt{\frac{x^{3}}{2-x}})
(dy)/(dx)=0.276y-0.0012y^2	\frac{dy}{dx}=0.276y-0.0012y^{2}
integral of x/(x^8-1)	\int\:\frac{x}{x^{8}-1}dx
derivative of f(x)=ln(x^2+2)	derivative\:f(x)=\ln(x^{2}+2)
y^{''}+9y^'+18y=2050e^{2t}cos(10t)	y^{\prime\:\prime\:}+9y^{\prime\:}+18y=2050e^{2t}\cos(10t)
integral from-3 to 1 of sqrt(x+3)	\int\:_{-3}^{1}\sqrt{x+3}dx
normal of y=2x^3-3x+1,(1,0)	normal\:y=2x^{3}-3x+1,(1,0)
derivative of-xsin(x+cos(x))	\frac{d}{dx}(-x\sin(x)+\cos(x))
integral of 1/(3+cos(x))	\int\:\frac{1}{3+\cos(x)}dx
integral from-pi to pi of \|sin(x)\|	\int\:_{-π}^{π}\left\|\sin(x)\right\|dx
y^'=(3x-2)(30x+19)	y^{\prime\:}=(3x-2)(30x+19)
(\partial)/(\partial x)(400sin(x)cos(x))	\frac{\partial\:}{\partial\:x}(400\cdot\:\sin(x)\cdot\:\cos(x))
(\partial)/(\partial x)(y^2e^{xy^2+z^2})	\frac{\partial\:}{\partial\:x}(y^{2}e^{xy^{2}+z^{2}})
y^'=x^2e^{2y},y(-1)=-1	y^{\prime\:}=x^{2}e^{2y},y(-1)=-1
d/(dt)(3cos(t)-2e^{2t})	\frac{d}{dt}(3\cos(t)-2e^{2t})
slope ofintercept (-1,0),(0,-2)	slopeintercept\:(-1,0),(0,-2)
(x^2+3xy+y^2)dx-x^2dy=0	(x^{2}+3xy+y^{2})dx-x^{2}dy=0
taylor cos(x),-pi/2	taylor\:\cos(x),-\frac{π}{2}
area 5/x ,y=3x,y= 1/3 x	area\:\frac{5}{x},y=3x,y=\frac{1}{3}x
integral from a to b of 1/(x^2)	\int\:_{a}^{b}\frac{1}{x^{2}}dx
integral from 0 to 2 of x^2(2-x)^2	\int\:_{0}^{2}x^{2}(2-x)^{2}dx
integral of (e^{x/2})/(e^x)	\int\:\frac{e^{\frac{x}{2}}}{e^{x}}dx
slope of (-1,2),(1,-4)	slope\:(-1,2),(1,-4)
integral of 2x+4x^{-2}	\int\:2x+4x^{-2}dx
limit as x approaches 6 of 9x+\|x-6\|	\lim\:_{x\to\:6}(9x+\left\|x-6\right\|)
integral of x/(sqrt(8-x^2))	\int\:\frac{x}{\sqrt{8-x^{2}}}dx
derivative of y=3^x	derivative\:y=3^{x}
(dy)/(dx)=(xy+y+x+1)/(xy+2x-y-2)	\frac{dy}{dx}=\frac{xy+y+x+1}{xy+2x-y-2}
derivative of (x-4/(-x^2+4))	\frac{d}{dx}(\frac{x-4}{-x^{2}+4})

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