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Popular Calculus Problems

derivative of sqrt(1-169x^2)arccos(13x)	\frac{d}{dx}(\sqrt{1-169x^{2}}\arccos(13x))
derivative of (9x^2+9sqrt(x))/(8x)	derivative\:\frac{9x^{2}+9\sqrt{x}}{8x}
integral of 1/(2-t)+1/(2+t)	\int\:\frac{1}{2-t}+\frac{1}{2+t}dt
integral from-infinity to 4 of e^{-x}	\int\:_{-\infty\:}^{4}e^{-x}dx
y^{''}+y^'=sin^2(x)	y^{\prime\:\prime\:}+y^{\prime\:}=\sin^{2}(x)
area x=-2,x=1,y=11x,y=x^2-12	area\:x=-2,x=1,y=11x,y=x^{2}-12
derivative of sqrt(400-5x)	\frac{d}{dx}(\sqrt{400-5x})
integral of v(u+v^2)^4	\int\:v(u+v^{2})^{4}du
integral of sin(θ)	\int\:\sin(θ)dθ
derivative of sqrt(6)x+sqrt(7x)	\frac{d}{dx}(\sqrt{6}x+\sqrt{7x})
(\partial)/(\partial x)(-2sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(-2\sqrt{x^{2}+y^{2}})
derivative of x^{-4/3}	\frac{d}{dx}(x^{-\frac{4}{3}})
y^'+ky=e^{-7kx}	y^{\prime\:}+ky=e^{-7kx}
derivative of 1/(sqrt(64+5t^2))	derivative\:\frac{1}{\sqrt{64+5t^{2}}}
integral of 1/(x^2+9)	\int\:\frac{1}{x^{2}+9}dx
tangent of f(x)=2x^3-x^2+3x,\at x=1	tangent\:f(x)=2x^{3}-x^{2}+3x,\at\:x=1
integral from 0 to t of e^xsin(pix)	\int\:_{0}^{t}e^{x}\cdot\:\sin(π\cdot\:x)dx
tangent of 6e^xcos(x)	tangent\:6e^{x}\cos(x)
limit as x approaches 6 of x^2-36	\lim\:_{x\to\:6}(x^{2}-36)
(\partial)/(\partial x)(sqrt(5x))	\frac{\partial\:}{\partial\:x}(\sqrt{5x})
limit as x approaches 0 of ((tan(5x)))/x	\lim\:_{x\to\:0}(\frac{(\tan(5x))}{x})
integral of 12x^2ln(x)	\int\:12x^{2}\ln(x)dx
derivative of arccot(15y)	derivative\:\arccot(15y)
derivative of (3sqrt(x)/2)	\frac{d}{dx}(\frac{3\sqrt{x}}{2})
x^2y^'+2xy=13cos^2(x)	x^{2}y^{\prime\:}+2xy=13\cos^{2}(x)
y^'+3x^2y=6x^2	y^{\prime\:}+3x^{2}y=6x^{2}
integral of-cot(2x)	\int\:-\cot(2x)dx
integral of sqrt(x)(sqrt(a)-sqrt(x))^2	\int\:\sqrt{x}(\sqrt{a}-\sqrt{x})^{2}dx
derivative of 2/(sqrt(x^2+1))	\frac{d}{dx}(\frac{2}{\sqrt{x^{2}+1}})
integral from 0 to 2 of 2pi(5-x)(8-x^3)	\int\:_{0}^{2}2π(5-x)(8-x^{3})dx
integral of (4/(x^2))	\int\:(\frac{4}{x^{2}})dx
(xdy)/(dx)+5y=7x^2,f(2)=5	\frac{xdy}{dx}+5y=7x^{2},f(2)=5
derivative of Cxe^{-x}	\frac{d}{dx}(Cxe^{-x})
integral of-16cos(4t+pi)	\int\:-16\cos(4t+π)dt
derivative of (x-2^{x+1})	\frac{d}{dx}((x-2)^{x+1})
(y^{-2})^'	(y^{-2})^{\prime\:}
(\partial)/(\partial x)(x^6y-2x^3y^2)	\frac{\partial\:}{\partial\:x}(x^{6}y-2x^{3}y^{2})
area y=x+4,y=x^2+x-12	area\:y=x+4,y=x^{2}+x-12
area 2(x+1),3(x+1),x=4	area\:2(x+1),3(x+1),x=4
derivative of x^3+x+3	derivative\:x^{3}+x+3
area e^x,e^{-4x},x=ln(3)	area\:e^{x},e^{-4x},x=\ln(3)
integral from 1 to 3 of ((x)^3+e^{-3x})	\int\:_{1}^{3}((x)^{3}+e^{-3x})dx
limit as x approaches 36 of sqrt(x)	\lim\:_{x\to\:36}(\sqrt{x})
limit as x approaches 3 of (4x+5)(3x-2)	\lim\:_{x\to\:3}((4x+5)(3x-2))
limit as x approaches-infinity of 1+x^2	\lim\:_{x\to\:-\infty\:}(1+x^{2})
y=xln(x)	y=x\ln(x)
tangent of f(x)=3sqrt(x),\at x=16	tangent\:f(x)=3\sqrt{x},\at\:x=16
integral of sec^3(2x)	\int\:\sec^{3}(2x)dx
integral from 0 to 4 of 4y-y^2	\int\:_{0}^{4}4y-y^{2}dy
inverse oflaplace (400)/((s(s^2+200)))	inverselaplace\:\frac{400}{(s(s^{2}+200))}
laplacetransform x^2e^{3x}	laplacetransform\:x^{2}e^{3x}
derivative of (arctan(2x)^2)	\frac{d}{dx}((\arctan(2x))^{2})
integral of ((x-1))/(x^2)	\int\:\frac{(x-1)}{x^{2}}dx
derivative of x^2sqrt(x)-5x	\frac{d}{dx}(x^{2}\sqrt{x}-5x)
area y=2-e^x,y=10e^{-x}-5	area\:y=2-e^{x},y=10e^{-x}-5
derivative of f(x)=(ln(4))/3 e^x	derivative\:f(x)=\frac{\ln(4)}{3}e^{x}
derivative of y=(5x-2)/(sqrt(x))	derivative\:y=\frac{5x-2}{\sqrt{x}}
tangent of 8x^{-2}	tangent\:8x^{-2}
integral of-sqrt(x)	\int\:-\sqrt{x}dx
limit as x approaches 0 of arccot(1/x)	\lim\:_{x\to\:0}(\arccot(\frac{1}{x}))
derivative of (-x^2+2x(3x+2)(x-1))	\frac{d}{dx}((-x^{2}+2x)(3x+2)(x-1))
tangent of f(x)=3x^2,(1,3)	tangent\:f(x)=3x^{2},(1,3)
y^'=(e^x)/y	y^{\prime\:}=\frac{e^{x}}{y}
integral from 1 to 5 of 2/x	\int\:_{1}^{5}\frac{2}{x}dx
limit as x approaches 0 of (20)/(1+x)	\lim\:_{x\to\:0}(\frac{20}{1+x})
integral of cos(5)	\int\:\cos(5)
integral of e^x*1/x	\int\:e^{x}\cdot\:\frac{1}{x}dx
derivative of y=cos(7x)	derivative\:y=\cos(7x)
slope of y=((x-4))/(sqrt(x)-2)	slope\:y=\frac{(x-4)}{\sqrt{x}-2}
sum from n=1 to infinity of 3*(4/3)^n	\sum\:_{n=1}^{\infty\:}3\cdot\:(\frac{4}{3})^{n}
y^{''}+2y^'+y=4e^{-2t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e^{-2t}
tangent of sqrt(x)(81.9)	tangent\:\sqrt{x}(81.9)
(1+x)^2y^'+(1+x)y=1	(1+x)^{2}y^{\prime\:}+(1+x)y=1
integral of 1/((x-2)sqrt(x+2))	\int\:\frac{1}{(x-2)\sqrt{x+2}}dx
laplacetransform (t-(3pi)/6)sin(6t)	laplacetransform\:(t-\frac{3π}{6})\sin(6t)
derivative of 6ln(cos(x))	\frac{d}{dx}(6\ln(\cos(x)))
(\partial)/(\partial x)(e^{xy}sin(y))	\frac{\partial\:}{\partial\:x}(e^{xy}\sin(y))
limit as x approaches 0 of 9x^2-2x+5	\lim\:_{x\to\:0}(9x^{2}-2x+5)
(\partial)/(\partial b)(10^{-2b})	\frac{\partial\:}{\partial\:b}(10^{-2b})
integral of (x^2)/(x^2+x-6)	\int\:\frac{x^{2}}{x^{2}+x-6}dx
limit as x approaches 0 of (sin(-x))/x	\lim\:_{x\to\:0}(\frac{\sin(-x)}{x})
derivative of e^x+cos(x)	\frac{d}{dx}(e^{x}+\cos(x))
derivative of 10log_{10}(100x)	\frac{d}{dx}(10\log_{10}(100x))
derivative of cos(2x^2-3)	\frac{d}{dx}(\cos(2x^{2}-3))
derivative of f(x)=(x^2)/(2+x)	derivative\:f(x)=\frac{x^{2}}{2+x}
area x^2-2x,x+4	area\:x^{2}-2x,x+4
area y=x^2-1,y=-x^2+1	area\:y=x^{2}-1,y=-x^{2}+1
sin(2x)dx+cos(3y)dy=0	\sin(2x)dx+\cos(3y)dy=0
derivative of (4-3x/(3x^2+x))	\frac{d}{dx}(\frac{4-3x}{3x^{2}+x})
(\partial}{\partial x}(\frac{7x)/y)	\frac{\partial\:}{\partial\:x}(\frac{7x}{y})
(dx)/(dy)-0.06x=200	\frac{dx}{dy}-0.06x=200
integral of (6x)/(sqrt(1-x^4))	\int\:\frac{6x}{\sqrt{1-x^{4}}}dx
integral from-3 to x of t^2e^{t^2}	\int\:_{-3}^{x}t^{2}e^{t^{2}}dt
integral from 1 to 2 of 5^{-θ}	\int\:_{1}^{2}5^{-θ}dθ
(\partial)/(\partial x)(x^2+y^2+1)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+1)
(d^2)/(dx^2)(xe^{-x})	\frac{d^{2}}{dx^{2}}(xe^{-x})
inverse oflaplace (1+s)/((s(s^2+s+1)))	inverselaplace\:\frac{1+s}{(s(s^{2}+s+1))}
integral of (cos(x))/((sin^2(x)+25)^2)	\int\:\frac{\cos(x)}{(\sin^{2}(x)+25)^{2}}dx
(\partial)/(\partial y)(2xy+y^2)	\frac{\partial\:}{\partial\:y}(2xy+y^{2})
x(dy)/(dx)+(-1+x)y=-xy^2	x\frac{dy}{dx}+(-1+x)y=-xy^{2}

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