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Popular Calculus Problems

tangent of f(x)=tan(x),(pi/4 ,1)	tangent\:f(x)=\tan(x),(\frac{π}{4},1)
integral of 4/(sqrt(x^2+2x+5))	\int\:\frac{4}{\sqrt{x^{2}+2x+5}}dx
y(1+x^2)y^'-x(8+y^2)=0	y(1+x^{2})y^{\prime\:}-x(8+y^{2})=0
maclaurin a^x	maclaurin\:a^{x}
(\partial)/(\partial x)(ln(x^2+x))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+x))
(\partial)/(\partial x)(4x-4-y^2)	\frac{\partial\:}{\partial\:x}(4x-4-y^{2})
derivative of (85t)/(99t-85)	derivative\:\frac{85t}{99t-85}
limit as x approaches 3 of x^2+2x-1	\lim\:_{x\to\:3}(x^{2}+2x-1)
v+x*(dv)/(dx)=x^2-1+2v	v+x\cdot\:\frac{dv}{dx}=x^{2}-1+2v
derivative of bcos(x)+x^2sin(x)	derivative\:b\cos(x)+x^{2}\sin(x)
derivative of ((x^2-1)/((x^2+x+1)))	\frac{d}{dx}(\frac{(x^{2}-1)}{(x^{2}+x+1)})
integral of sqrt(18-x^2)	\int\:\sqrt{18-x^{2}}dx
derivative of arccot(3x)	\frac{d}{dx}(\arccot(3x))
derivative of x^{5/3}-x^{2/3}	derivative\:x^{\frac{5}{3}}-x^{\frac{2}{3}}
derivative of x-3	derivative\:x-3
derivative of f(t)=t^{2/3}-t^{1/3}+4	derivative\:f(t)=t^{\frac{2}{3}}-t^{\frac{1}{3}}+4
limit as x approaches 3 of 5x-3	\lim\:_{x\to\:3}(5x-3)
integral of xarctan(6x)	\int\:x\arctan(6x)dx
(\partial)/(\partial y)(x^2yz)	\frac{\partial\:}{\partial\:y}(x^{2}yz)
(\partial)/(\partial r)(rcos(t))	\frac{\partial\:}{\partial\:r}(r\cos(t))
sum from n=1 to infinity of (n^6)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{6}}{6^{n}}
integral of w/(w^3+w^2+4w+4)	\int\:\frac{w}{w^{3}+w^{2}+4w+4}dw
integral of e^{-3x}sin(x)	\int\:e^{-3x}\sin(x)dx
integral from-2 to 1 of 1/(x+3)	\int\:_{-2}^{1}\frac{1}{x+3}dx
limit as x approaches 0+of (x^2)/7-2/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{7}-\frac{2}{x})
limit as x approaches 0 of (1+3x)^{2/3}	\lim\:_{x\to\:0}((1+3x)^{\frac{2}{3}})
integral of (x^2+2x+3)cos(2x)	\int\:(x^{2}+2x+3)\cos(2x)dx
integral from-infinity to 0 of 5^x	\int\:_{-\infty\:}^{0}5^{x}dx
integral from 2 to 4 of (x^2+8)/(x^2)	\int\:_{2}^{4}\frac{x^{2}+8}{x^{2}}dx
integral of ((6x^512x^4+9x^3)/(3x^2))	\int\:(\frac{6x^{5}12x^{4}+9x^{3}}{3x^{2}})dx
inverse oflaplace 1/((s^2+1)(s^2+4s+8))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2}+4s+8)}
derivative of f(x)=sqrt(x^2+5)	derivative\:f(x)=\sqrt{x^{2}+5}
yy^'-16e^x=0	yy^{\prime\:}-16e^{x}=0
d/(dy)(e^{-y^2})	\frac{d}{dy}(e^{-y^{2}})
derivative of (x^2-x+1/(x^2+x+1))	\frac{d}{dx}(\frac{x^{2}-x+1}{x^{2}+x+1})
tangent of x^3-6x^2+5x	tangent\:x^{3}-6x^{2}+5x
integral of 1/(2x-4)	\int\:\frac{1}{2x-4}dx
(\partial)/(\partial x)(xt)	\frac{\partial\:}{\partial\:x}(xt)
integral of 2x^3+1	\int\:2x^{3}+1dx
integral of csc^2(3x)	\int\:\csc^{2}(3x)dx
derivative of 1/7 sin(7x)	derivative\:\frac{1}{7}\sin(7x)
tangent of y=2sin(x)	tangent\:y=2\sin(x)
d/(dt)(e^t*sin(t))	\frac{d}{dt}(e^{t}\cdot\:\sin(t))
(\partial)/(\partial x)(0.1sqrt(x)y)	\frac{\partial\:}{\partial\:x}(0.1\cdot\:\sqrt{x}\cdot\:y)
integral of 3xe^{-2x}	\int\:3xe^{-2x}dx
integral of 1/7 x	\int\:\frac{1}{7}xdx
derivative of (10x+20)/x	derivative\:\frac{10x+20}{x}
integral of tan^3(6x)sec(6x)	\int\:\tan^{3}(6x)\sec(6x)dx
integral of sqrt(y^2-x^2)	\int\:\sqrt{y^{2}-x^{2}}dx
limit as x approaches-2 of sqrt(25-5x)	\lim\:_{x\to\:-2}(\sqrt{25-5x})
derivative of f(x)=x^{4/3}-4x^{1/3}+1	derivative\:f(x)=x^{\frac{4}{3}}-4x^{\frac{1}{3}}+1
derivative of x^2sqrt(5-x)	\frac{d}{dx}(x^{2}\sqrt{5-x})
derivative of x^4sec(5/x)	derivative\:x^{4}\sec(\frac{5}{x})
limit as z approaches 0 of 1/(f(z) 1/z)	\lim\:_{z\to\:0}(\frac{1}{f(z)\frac{1}{z}})
derivative of sqrt(x+4)	derivative\:\sqrt{x+4}
sum from n=1 to infinity of nsin(pin)	\sum\:_{n=1}^{\infty\:}n\cdot\:\sin(π\cdot\:n)
integral of (ln(ln(5x)))/(5x)	\int\:\frac{\ln(\ln(5x))}{5x}dx
derivative of (x^2+6)^9	derivative\:(x^{2}+6)^{9}
(\partial)/(\partial z)(-xy)	\frac{\partial\:}{\partial\:z}(-xy)
ty^{''}+y^'=0	ty^{\prime\:\prime\:}+y^{\prime\:}=0
tangent of f(x)=7x-4x^2,(-3,-57)	tangent\:f(x)=7x-4x^{2},(-3,-57)
derivative of e^x(2x^4-1)	\frac{d}{dx}(e^{x}(2x^{4}-1))
(d^2)/(dx^2)(2x)	\frac{d^{2}}{dx^{2}}(2x)
integral of sqrt(x)*ln(x)	\int\:\sqrt{x}\cdot\:\ln(x)dx
integral from-4 to 0 of (1+sqrt(16-x^2))	\int\:_{-4}^{0}(1+\sqrt{16-x^{2}})dx
integral of t^2sqrt(13t-1)	\int\:t^{2}\sqrt{13t-1}dt
derivative of f(x)=(4/x)+(1/(5x^3+2x))	derivative\:f(x)=(\frac{4}{x})+(\frac{1}{5x^{3}+2x})
integral from 0 to pi/2 of sec^2(x/2)	\int\:_{0}^{\frac{π}{2}}\sec^{2}(\frac{x}{2})dx
xy^'-2y=0	xy^{\prime\:}-2y=0
y^'+y=4x	y^{\prime\:}+y=4x
integral of 2x+1/(x^2)+2x-3	\int\:2x+\frac{1}{x^{2}}+2x-3dx
taylor 1/(2x),1	taylor\:\frac{1}{2x},1
derivative of cos((ln(x+1)^2-e^{x^2}))	\frac{d}{dx}(\cos((\ln(x+1))^{2}-e^{x^{2}}))
(\partial)/(\partial x)(2x^{1/2}y^{1/4})	\frac{\partial\:}{\partial\:x}(2x^{\frac{1}{2}}y^{\frac{1}{4}})
derivative of x^3-(x^2)/(40)	derivative\:x^{3}-\frac{x^{2}}{40}
y^'=4+2sin(x/4)-y/(100)	y^{\prime\:}=4+2\sin(\frac{x}{4})-\frac{y}{100}
integral of 1/(n(ln(n))^2)	\int\:\frac{1}{n(\ln(n))^{2}}
integral from 0 to 1 of (3-4x)e^{2x}	\int\:_{0}^{1}(3-4x)e^{2x}dx
y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0	y^{\prime\:\prime\:}+\frac{200}{8}\cdot\:y=30\sin(2x),y(0)=2,y^{\prime\:}(0)=0
derivative of-c/(x^2)	\frac{d}{dx}(-\frac{c}{x^{2}})
tangent of (2x+1)/(x+2)	tangent\:\frac{2x+1}{x+2}
laplacetransform 3t^4e^{-2t}	laplacetransform\:3t^{4}e^{-2t}
area x^5,e^3x^2	area\:x^{5},e^{3}x^{2}
inverse oflaplace (2s-3)/(s^2+4)	inverselaplace\:\frac{2s-3}{s^{2}+4}
y^'+xy=1xy^3	y^{\prime\:}+xy=1xy^{3}
integral from 1 to 6 of-x^2+7x-6	\int\:_{1}^{6}-x^{2}+7x-6dx
limit as x approaches 2+of (6x)/(x-2)	\lim\:_{x\to\:2+}(\frac{6x}{x-2})
(\partial)/(\partial x)(ln(1+x^2)-2e^{5y})	\frac{\partial\:}{\partial\:x}(\ln(1+x^{2})-2e^{5y})
integral of 1/(x(ln(x))^p)	\int\:\frac{1}{x(\ln(x))^{p}}dx
d/(d{y)}(c{y}^{-6})	\frac{d}{d{y}}(c{y}^{-6})
limit as x approaches 0 of cos(x)-sin(x)	\lim\:_{x\to\:0}(\cos(x)-\sin(x))
derivative of (e^x/(5x))	\frac{d}{dx}(\frac{e^{x}}{5x})
integral of-3arcsin(10x)	\int\:-3\arcsin(10x)dx
slope ofintercept (-5,-2),(5,4)	slopeintercept\:(-5,-2),(5,4)
integral of arcsin(x)x	\int\:\arcsin(x)xdx
limit as x approaches-3 of 2x^3+5x^2-25	\lim\:_{x\to\:-3}(2x^{3}+5x^{2}-25)
y^'=(2y)/x ,y(1)=2	y^{\prime\:}=\frac{2y}{x},y(1)=2
integral from 0 to 1 of x/(e^{2x)}	\int\:_{0}^{1}\frac{x}{e^{2x}}dx
derivative of-9.8x^2+2x+1	derivative\:-9.8x^{2}+2x+1
integral from 1 to 2 of 4/(2x+3)	\int\:_{1}^{2}\frac{4}{2x+3}dx

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