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Popular Calculus Problems

integral from 0 to 4 of xe^{sqrt(x)}	\int\:_{0}^{4}xe^{\sqrt{x}}dx
d/(dt)((t^3)/6+(t^2)/4+1/2 t)	\frac{d}{dt}(\frac{t^{3}}{6}+\frac{t^{2}}{4}+\frac{1}{2}t)
integral of (sec(x)tan(x))/(sec(x)-7)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)-7}dx
d/(dθ)(-2sin(θ))	\frac{d}{dθ}(-2\sin(θ))
laplacetransform e^tsin(t)	laplacetransform\:e^{t}\sin(t)
(\partial)/(\partial x)(4x^{-1/8})	\frac{\partial\:}{\partial\:x}(4x^{-\frac{1}{8}})
integral of 3x^2e^{-3x}	\int\:3x^{2}e^{-3x}dx
derivative of 6x^2(4x^5-3x+2)	\frac{d}{dx}(6x^{2}(4x^{5}-3x+2))
limit as x approaches 0+of x^3(ln(x))^2	\lim\:_{x\to\:0+}(x^{3}(\ln(x))^{2})
derivative of y=x(1+x^2)^{10}	derivative\:y=x(1+x^{2})^{10}
limit as x approaches 0-of x/x	\lim\:_{x\to\:0-}(\frac{x}{x})
integral of (3y-4y^3)^3	\int\:(3y-4y^{3})^{3}dy
tangent of y=ln(x/2),\at x=4	tangent\:y=\ln(\frac{x}{2}),\at\:x=4
integral of (t^2)/(t+1)	\int\:\frac{t^{2}}{t+1}dt
derivative of lx	\frac{d}{dx}(lx)
derivative of arccos(-3x)	\frac{d}{dx}(\arccos(-3x))
y^{''}+16=0	y^{\prime\:\prime\:}+16=0
derivative of ((e^{-x^2})/(x^3))	\frac{d}{dx}(\frac{(e^{-x^{2}})}{x^{3}})
integral of x/4	\int\:\frac{x}{4}dx
limit as x approaches 8 of (\|x-8\|)/(x-8)	\lim\:_{x\to\:8}(\frac{\left\|x-8\right\|}{x-8})
limit as x approaches 6+of (2+x)/(6-x)	\lim\:_{x\to\:6+}(\frac{2+x}{6-x})
derivative of f(x)=3x^{2x+3}+e^2	derivative\:f(x)=3x^{2x+3}+e^{2}
limit as x approaches 0 of e^xsin(x)	\lim\:_{x\to\:0}(e^{x}\sin(x))
integral of 2/(x(x^2+1))	\int\:\frac{2}{x(x^{2}+1)}dx
integral of yx^2	\int\:yx^{2}dy
(\partial)/(\partial x)(3x+2y)	\frac{\partial\:}{\partial\:x}(3x+2y)
integral of (x^2+x-5)/(2x^3+3x^2-2x)	\int\:\frac{x^{2}+x-5}{2x^{3}+3x^{2}-2x}dx
integral of cos(ln(2x))	\int\:\cos(\ln(2x))dx
integral of x/(x^2-2x+5)	\int\:\frac{x}{x^{2}-2x+5}dx
derivative of arccot(x/4)	\frac{d}{dx}(\arccot(\frac{x}{4}))
integral of (y^3)/((2+3y^4)^3)	\int\:\frac{y^{3}}{(2+3y^{4})^{3}}dy
derivative of sin(tan(3x))	derivative\:\sin(\tan(3x))
derivative of log_{4}(e^{2x}cos(3x))	derivative\:\log_{4}(e^{2x}\cos(3x))
tangent of (30x^2)/((-5x^3+4)^3)	tangent\:\frac{30x^{2}}{(-5x^{3}+4)^{3}}
slope of x^2+xy-y^2=-11,(1,4)	slope\:x^{2}+xy-y^{2}=-11,(1,4)
t^2y^{''}+3ty^'-3y= 1/t	t^{2}y^{\prime\:\prime\:}+3ty^{\prime\:}-3y=\frac{1}{t}
derivative of 2/(x-3)	derivative\:\frac{2}{x-3}
integral of cos(x)(7+8sin^2(x))	\int\:\cos(x)(7+8\sin^{2}(x))dx
6y^{''}+40y^'+54y=0	6y^{\prime\:\prime\:}+40y^{\prime\:}+54y=0
derivative of-kx	\frac{d}{dx}(-kx)
integral of cos(x)-xsin(x)	\int\:\cos(x)-x\sin(x)dx
derivative of e^{-x^{62}}	derivative\:e^{-x^{62}}
y^'=x-2y	y^{\prime\:}=x-2y
slope of (1,4),(-5,2)	slope\:(1,4),(-5,2)
integral of 1/(sqrt(12x-9x^2-2))	\int\:\frac{1}{\sqrt{12x-9x^{2}-2}}dx
derivative of 3xy	derivative\:3xy
(\partial)/(\partial x)(45ysin(9x))	\frac{\partial\:}{\partial\:x}(45y\sin(9x))
integral from 1 to 3 of (y^4+1/(4y^4))	\int\:_{1}^{3}(y^{4}+\frac{1}{4y^{4}})dy
y^{''}+6y^'+25y=0,y(0)=a,y^'(0)=b	y^{\prime\:\prime\:}+6y^{\prime\:}+25y=0,y(0)=a,y^{\prime\:}(0)=b
integral from 3 to 7 of 1	\int\:_{3}^{7}1dx
integral from 0 to 6 of 1/18 x	\int\:_{0}^{6}\frac{1}{18}xdx
derivative of xpi	\frac{d}{dx}(xπ)
inverse oflaplace 1/((s+3)^2)	inverselaplace\:\frac{1}{(s+3)^{2}}
tangent of (5x)/(sqrt(4-x^2))	tangent\:\frac{5x}{\sqrt{4-x^{2}}}
derivative of 8x^2cos(x)cot(x)	derivative\:8x^{2}\cos(x)\cot(x)
y^'=(6x^6e^{y/x}+x^4y^2)/(x^5y)	y^{\prime\:}=\frac{6x^{6}e^{\frac{y}{x}}+x^{4}y^{2}}{x^{5}y}
integral of (x^2-7x+5)	\int\:(x^{2}-7x+5)dx
derivative of (4-2x-x^3/(3x-x^4))	\frac{d}{dx}(\frac{4-2x-x^{3}}{3x-x^{4}})
volumeabout y=0,y=9-x^2,y=0	volumeabout\:y=0,y=9-x^{2},y=0
tangent of f(x)= 1/(x^4),(3, 1/81)	tangent\:f(x)=\frac{1}{x^{4}},(3,\frac{1}{81})
integral of (4/(x^3)+2)/(1/(x^2)-x)	\int\:\frac{\frac{4}{x^{3}}+2}{\frac{1}{x^{2}}-x}dx
derivative of f(x)=6xarcsin(x)	derivative\:f(x)=6x\arcsin(x)
(\partial)/(\partial x)(arcsin(4xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(4xyz))
tangent of f(x)=sqrt(18x+18),(1,6)	tangent\:f(x)=\sqrt{18x+18},(1,6)
(2xy+2y^2)dx+(x^2+4xy)dy=0	(2xy+2y^{2})dx+(x^{2}+4xy)dy=0
derivative of x^3(x-2)^2	derivative\:x^{3}(x-2)^{2}
integral of 27x^2	\int\:27x^{2}dx
integral of 6\sqrt[4]{x}	\int\:6\sqrt[4]{x}dx
integral from-pi/4 to 0 of 4sec^3(x)	\int\:_{-\frac{π}{4}}^{0}4\sec^{3}(x)dx
(\partial)/(\partial x)(2x^2+{Y}(x)(x)^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+{Y}(x)(x)^{2})
integral of (2sqrt(x))/x	\int\:\frac{2\sqrt{x}}{x}dx
integral of (x+1)/(x^2-3x+2)	\int\:\frac{x+1}{x^{2}-3x+2}dx
tangent of x-2x^2	tangent\:x-2x^{2}
(d^3)/(dx^3)(e^{5x-4})	\frac{d^{3}}{dx^{3}}(e^{5x-4})
sum from n=1 to infinity of (n!)/(90^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{90^{n}}
limit as x approaches 2 of 2x^3-x^2+7x-3	\lim\:_{x\to\:2}(2x^{3}-x^{2}+7x-3)
derivative of 2tan(xsec(x))	\frac{d}{dx}(2\tan(x)\sec(x))
derivative of sqrt(-3x)	\frac{d}{dx}(\sqrt{-3x})
d/(dt)(t^3+1)	\frac{d}{dt}(t^{3}+1)
integral of x+e^z	\int\:x+e^{z}dx
limit as x approaches 3 of (x-1)^2(x+1)	\lim\:_{x\to\:3}((x-1)^{2}(x+1))
derivative of (1+sin(x)/(x+cos(x)))	\frac{d}{dx}(\frac{1+\sin(x)}{x+\cos(x)})
derivative of (e^x+e^{-x}/9)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{9})
implicit x^{2/3}+y^{2/3}=4	implicit\:x^{\frac{2}{3}}+y^{\frac{2}{3}}=4
integral of (x^2+x)	\int\:(x^{2}+x)dx
(\partial)/(\partial t)(sqrt(t))	\frac{\partial\:}{\partial\:t}(\sqrt{t})
(\partial)/(\partial x)(ln(y-x))	\frac{\partial\:}{\partial\:x}(\ln(y-x))
derivative of (x^6/(2-x^5))	\frac{d}{dx}(\frac{x^{6}}{2-x^{5}})
derivative of (2.5^x)	\frac{d}{dx}((2.5)^{x})
integral of (sqrt(64-x^2))/x	\int\:\frac{\sqrt{64-x^{2}}}{x}dx
tangent of f(x)=2x^2-3x,\at x=2	tangent\:f(x)=2x^{2}-3x,\at\:x=2
derivative of x^3-3x+5	\frac{d}{dx}(x^{3}-3x+5)
sum from n=1 to infinity of e^{-3/(n^2)}	\sum\:_{n=1}^{\infty\:}e^{-\frac{3}{n^{2}}}
integral from 1 to infinity of 3/(x^2+1)	\int\:_{1}^{\infty\:}\frac{3}{x^{2}+1}dx
integral of ((2x+1))/x	\int\:\frac{(2x+1)}{x}dx
sum from n=8 to infinity of (7/8)^{-n}	\sum\:_{n=8}^{\infty\:}(\frac{7}{8})^{-n}
(\partial)/(\partial z)(x^3+yz^2)	\frac{\partial\:}{\partial\:z}(x^{3}+yz^{2})
(\partial)/(\partial x)(cos(x/(1+y)))	\frac{\partial\:}{\partial\:x}(\cos(\frac{x}{1+y}))
limit as x approaches 2+of intx	\lim\:_{x\to\:2+}(intx)
d/(dθ)(sin^2(θ))	\frac{d}{dθ}(\sin^{2}(θ))

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