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Popular Calculus Problems

integral of x/(x^{-5/2)}	\int\:\frac{x}{x^{-\frac{5}{2}}}dx
integral of 3x^2-3y^2	\int\:3x^{2}-3y^{2}dy
d/(dt)(te^{(t)})	\frac{d}{dt}(te^{(t)})
limit as x approaches-1 of 4x^3-3x^2+5	\lim\:_{x\to\:-1}(4x^{3}-3x^{2}+5)
limit as x approaches 0= of (sin(4x))/6	\lim\:_{x\to\:0=}(\frac{\sin(4x)}{6})
limit as x approaches 6+of (cos((5pi)/6))/(ln(7-x))	\lim\:_{x\to\:6+}(\frac{\cos(\frac{5π}{6})}{\ln(7-x)})
laplacetransform H^{1/2}	laplacetransform\:H^{\frac{1}{2}}
limit as w approaches 3 of ((w-3))/((2w^2-w-15))	\lim\:_{w\to\:3}(\frac{(w-3)}{(2w^{2}-w-15)})
x^2y^'=xy+2x^2e^{y/x}	x^{2}y^{\prime\:}=xy+2x^{2}e^{\frac{y}{x}}
f(x)=-1/(1-x)	f(x)=-\frac{1}{1-x}
(\partial)/(\partial x)(-sin^2(x))	\frac{\partial\:}{\partial\:x}(-\sin^{2}(x))
derivative of arcsin({f}(x))	\frac{d}{dx}(\arcsin({f}(x)))
integral of sqrt(tan(4x))(sec(4x))^2	\int\:\sqrt{\tan(4x)}(\sec(4x))^{2}dx
limit as x approaches 1-of (x^2+1)^2	\lim\:_{x\to\:1-}((x^{2}+1)^{2})
laplacetransform \delta(t-1)	laplacetransform\:\delta(t-1)
integral from 0 to pi of cos(x+pi)	\int\:_{0}^{π}\cos(x+π)dx
integral of (x^2)/x	\int\:\frac{x^{2}}{x}dx
(\partial)/(\partial x)(3ax^2+e^{xx}+e^x)	\frac{\partial\:}{\partial\:x}(3ax^{2}+e^{xx}+e^{x})
integral of sqrt(x^2-4x+1)	\int\:\sqrt{x^{2}-4x+1}dx
derivative of (5x-x^2/(sqrt(x))-3cot(x))	\frac{d}{dx}(\frac{5x-x^{2}}{\sqrt{x}}-3\cot(x))
integral of (((y+1))/y)^2	\int\:(\frac{(y+1)}{y})^{2}dy
integral of 1/(x^2*sqrt(16+9x^2))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{16+9x^{2}}}dx
(\partial)/(\partial x)(1/2 ln(y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(y))
integral of 2/x-4e^x	\int\:\frac{2}{x}-4e^{x}dx
(\partial)/(\partial x)((3y)/(x^5))	\frac{\partial\:}{\partial\:x}(\frac{3y}{x^{5}})
integral from 2 to infinity of e^{-x/3}	\int\:_{2}^{\infty\:}e^{-\frac{x}{3}}dx
derivative of cos(sin(x^3))	derivative\:\cos(\sin(x^{3}))
y^3-(18x+4)+3xy^2y^'=0	y^{3}-(18x+4)+3xy^{2}y^{\prime\:}=0
(\partial)/(\partial x)(e^{-x}*(x-y^2))	\frac{\partial\:}{\partial\:x}(e^{-x}\cdot\:(x-y^{2}))
derivative of arcsech(sqrt(1-x^2))	\frac{d}{dx}(\arcsech(\sqrt{1-x^{2}}))
derivative of x*e^{xy}	\frac{d}{dx}(x\cdot\:e^{xy})
derivative of (cos^2(x)^x)	\frac{d}{dx}((\cos^{2}(x))^{x})
limit as x approaches 0-of x^3+3x+2	\lim\:_{x\to\:0-}(x^{3}+3x+2)
e^xy*(dy)/(dx)=e^{-y}+e^{-3x-y}	e^{x}y\cdot\:\frac{dy}{dx}=e^{-y}+e^{-3x-y}
limit as x approaches 0+of (tan(2x))^2	\lim\:_{x\to\:0+}((\tan(2x))^{2})
(\partial)/(\partial x)((x^{1-a})/(1-a))	\frac{\partial\:}{\partial\:x}(\frac{x^{1-a}}{1-a})
integral of (x^3+4x^2-5)/(x^3)	\int\:\frac{x^{3}+4x^{2}-5}{x^{3}}dx
derivative of acos(x+x^2sin(x))	\frac{d}{dx}(a\cos(x)+x^{2}\sin(x))
limit as x approaches 0 of (sin(3/5)x)/x	\lim\:_{x\to\:0}(\frac{\sin(\frac{3}{5})x}{x})
integral of cos^4(5x)	\int\:\cos^{4}(5x)dx
derivative of sin(2x+10)	\frac{d}{dx}(\sin(2x)+10)
derivative of 5/(x^2)	derivative\:\frac{5}{x^{2}}
integral from 0 to 1.75 of 1250x	\int\:_{0}^{1.75}1250xdx
y^'+3y=x^2	y^{\prime\:}+3y=x^{2}
derivative of x/((x+1^2))	\frac{d}{dx}(\frac{x}{(x+1)^{2}})
(dy)/(dx)+4e^{x+y}=0	\frac{dy}{dx}+4e^{x+y}=0
area y=x^2-9,y=(2x-1)(x+3)	area\:y=x^{2}-9,y=(2x-1)(x+3)
derivative of 9(3x+5^2)	\frac{d}{dx}(9(3x+5)^{2})
limit as (x,y) approaches (0,3) of x^3y	\lim\:_{(x,y)\to\:(0,3)}(x^{3}y)
derivative of ((x^3)^2)^2	derivative\:((x^{3})^{2})^{2}
(\partial)/(\partial x)(1/(y-1))	\frac{\partial\:}{\partial\:x}(\frac{1}{y-1})
integral of e^{2x}*2x	\int\:e^{2x}\cdot\:2xdx
derivative of ((x+3(x^2-3x+9))/(x^3))	\frac{d}{dx}(\frac{(x+3)(x^{2}-3x+9)}{x^{3}})
(dy)/(dx)=4y^2-3y+1	\frac{dy}{dx}=4y^{2}-3y+1
area x=y+12,x=y^2+2y	area\:x=y+12,x=y^{2}+2y
derivative of sin(tan(7x))	derivative\:\sin(\tan(7x))
integral from 2 to 4 of (10+4x-3x^3)	\int\:_{2}^{4}(10+4x-3x^{3})dx
derivative of f(x)=30e^{x^2}x	derivative\:f(x)=30e^{x^{2}}x
integral from 0 to 9 of 2piy(81-y^2)	\int\:_{0}^{9}2πy(81-y^{2})dy
integral of (x+1)/((x^2+2x-1)^2)	\int\:\frac{x+1}{(x^{2}+2x-1)^{2}}dx
limit as x approaches 2-of 5x^5-9x^4+5	\lim\:_{x\to\:2-}(5x^{5}-9x^{4}+5)
laplacetransform cos(2t-2)e^{3t}	laplacetransform\:\cos(2t-2)e^{3t}
integral from 0 to 1.75 of 1500x	\int\:_{0}^{1.75}1500xdx
integral of 1/(x^3-4x^2+8x)	\int\:\frac{1}{x^{3}-4x^{2}+8x}dx
limit as x approaches 3 of 1/(6-2x)	\lim\:_{x\to\:3}(\frac{1}{6-2x})
integral of (3x-1)/(x^2-3x-4)	\int\:\frac{3x-1}{x^{2}-3x-4}dx
integral of e^{2t+e^t}	\int\:e^{2t+e^{t}}dt
derivative of (5x^2-2x+1^{-3})	\frac{d}{dx}((5x^{2}-2x+1)^{-3})
integral of-5/(3x)	\int\:-\frac{5}{3x}dx
derivative of ((2x^4+5x^3-2x-8))/((x+3))	derivative\:\frac{(2x^{4}+5x^{3}-2x-8)}{(x+3)}
(\partial)/(\partial x)((4x-3t)/(s+2x))	\frac{\partial\:}{\partial\:x}(\frac{4x-3t}{s+2x})
(\partial)/(\partial x)(x-cos(x))	\frac{\partial\:}{\partial\:x}(x-\cos(x))
y^'=yx	y^{\prime\:}=yx
limit as x approaches 0 of+(x^3+3)/x	\lim\:_{x\to\:0}(+\frac{x^{3}+3}{x})
derivative of ln(3-x^2)	\frac{d}{dx}(\ln(3-x^{2}))
derivative of sqrt(24+x^2)	\frac{d}{dx}(\sqrt{24+x^{2}})
derivative of e^{(-1/x})	\frac{d}{dx}(e^{\frac{-1}{x}})
limit as x approaches 0 of 10^x	\lim\:_{x\to\:0}(10^{x})
limit as x approaches 3 of (x^2-2)/(3-x)	\lim\:_{x\to\:3}(\frac{x^{2}-2}{3-x})
tangent of y=(x^3-4x)^{10}	tangent\:y=(x^{3}-4x)^{10}
derivative of 5/2 x	\frac{d}{dx}(\frac{5}{2}x)
tangent of 3/(sin(x)+cos(x))	tangent\:\frac{3}{\sin(x)+\cos(x)}
y^'=x+y,y(0)=5	y^{\prime\:}=x+y,y(0)=5
integral of x/((x-2)^2)	\int\:\frac{x}{(x-2)^{2}}dx
limit as x approaches-infinity of x-1	\lim\:_{x\to\:-\infty\:}(x-1)
(\partial ^2)/(\partial x^2)(xy^2-6x^2-3y^2)	\frac{\partial\:^{2}}{\partial\:x^{2}}(xy^{2}-6x^{2}-3y^{2})
derivative of (2x^2+x-3)/(-3x^2-4x+2)	derivative\:\frac{2x^{2}+x-3}{-3x^{2}-4x+2}
simplify (e^{-x}-e^5)(e^x+e^{-3})	simplify\:(e^{-x}-e^{5})(e^{x}+e^{-3})
inverse oflaplace (400)/(s(s+2)^3)	inverselaplace\:\frac{400}{s(s+2)^{3}}
(\partial)/(\partial x)(6x^{y/z})	\frac{\partial\:}{\partial\:x}(6x^{\frac{y}{z}})
derivative of x^2-2xe^{-x}+e^{-2x}	\frac{d}{dx}(x^{2}-2xe^{-x}+e^{-2x})
integral from 0 to 2 of \|x\|	\int\:_{0}^{2}\left\|x\right\|dx
limit as x approaches 0 of x(e^x-1/x)	\lim\:_{x\to\:0}(x(e^{x}-\frac{1}{x}))
tangent of f(x)=x^2+3x-3,\at x=1	tangent\:f(x)=x^{2}+3x-3,\at\:x=1
derivative of 15(cos(x)-xsin(x))	derivative\:15(\cos(x)-x\sin(x))
limit as x approaches 1-of 6/(x^3-1)	\lim\:_{x\to\:1-}(\frac{6}{x^{3}-1})
9y^{''}+48y^'+64y=0	9y^{\prime\:\prime\:}+48y^{\prime\:}+64y=0
f^'(x)=-x	f^{\prime\:}(x)=-x
derivative of (arctan(9x)^2)	\frac{d}{dx}((\arctan(9x))^{2})
d/(dt)(acos(10t)+bsin(10t))	\frac{d}{dt}(a\cos(10t)+b\sin(10t))

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