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Popular Calculus Problems

integral of 4sin^6(x)cos(x)	\int\:4\sin^{6}(x)\cos(x)dx
limit as h approaches 1/2 of (8h^3-1)/(1-2h)	\lim\:_{h\to\:\frac{1}{2}}(\frac{8h^{3}-1}{1-2h})
derivative of 8/(tan^3(x/2))	derivative\:\frac{8}{\tan^{3}(\frac{x}{2})}
integral of cos(2X)	\int\:\cos(2X)dX
derivative of (-6x)/(x^2+1)	derivative\:\frac{-6x}{x^{2}+1}
derivative of (e^{2x-y}/(x^3))	\frac{d}{dx}(\frac{e^{2x-y}}{x^{3}})
derivative of f(x)= 1/((1-x)^2)	derivative\:f(x)=\frac{1}{(1-x)^{2}}
derivative of f(x)=4x^3-18x^2	derivative\:f(x)=4x^{3}-18x^{2}
y^'=4y(3-y)	y^{\prime\:}=4y(3-y)
integral of ye^{-yx}	\int\:ye^{-yx}dx
sum from n=0 to infinity of (-3/2)^{-2n}	\sum\:_{n=0}^{\infty\:}(-\frac{3}{2})^{-2n}
tangent of f(x)= 6/(3x+1),(-1,-3)	tangent\:f(x)=\frac{6}{3x+1},(-1,-3)
limit as x approaches 2 of ((\|x-2\|))/x	\lim\:_{x\to\:2}(\frac{(\left\|x-2\right\|)}{x})
integral of (3x^2-3x+2)	\int\:(3x^{2}-3x+2)dx
tangent of f(x)=sqrt(x)+1/(sqrt(x))	tangent\:f(x)=\sqrt{x}+\frac{1}{\sqrt{x}}
limit as x approaches-3-of-x+3	\lim\:_{x\to\:-3-}(-x+3)
derivative of 5x^{-1}	derivative\:5x^{-1}
(\partial)/(\partial x)(A^3(x/d)^2)	\frac{\partial\:}{\partial\:x}(A^{3}(\frac{x}{d})^{2})
derivative of (x^3/y)	\frac{d}{dx}(\frac{x^{3}}{y})
d/(dy)(ln(x^2+y^2))	\frac{d}{dy}(\ln(x^{2}+y^{2}))
derivative of 6/5 e^{-20x}	\frac{d}{dx}(\frac{6}{5}e^{-20x})
taylor ln(x/2),x=2	taylor\:\ln(\frac{x}{2}),x=2
limit as x approaches-1 of x^5-1	\lim\:_{x\to\:-1}(x^{5}-1)
derivative of (24x(-x^2+1)/((x^2+1)^4))	\frac{d}{dx}(\frac{24x(-x^{2}+1)}{(x^{2}+1)^{4}})
y^'=0.1ln((4000)/y)y,y(0)=500	y^{\prime\:}=0.1\ln(\frac{4000}{y})y,y(0)=500
derivative of 6pix^2	\frac{d}{dx}(6πx^{2})
derivative of e^{x/5}	\frac{d}{dx}(e^{\frac{x}{5}})
derivative of (2x+1^5)	\frac{d}{dx}((2x+1)^{5})
integral from 1 to t of 35x^{-3}	\int\:_{1}^{t}35x^{-3}dx
integral of (x^3)/(3(x^2+1))	\int\:\frac{x^{3}}{3(x^{2}+1)}dx
derivative of e^{tan(x)}	derivative\:e^{\tan(x)}
derivative of f(x)= x/(x^2+64)	derivative\:f(x)=\frac{x}{x^{2}+64}
laplacetransform 2(1-e^{-t})	laplacetransform\:2(1-e^{-t})
sum from n=1 to infinity of n(3/4)^n	\sum\:_{n=1}^{\infty\:}n(\frac{3}{4})^{n}
derivative of f(x)=(sin(x))/(x^2)	derivative\:f(x)=\frac{\sin(x)}{x^{2}}
derivative of y=(5/x+x)(5/x-x)	derivative\:y=(\frac{5}{x}+x)(\frac{5}{x}-x)
y^{''}+y^'-2=e^{-t}	y^{\prime\:\prime\:}+y^{\prime\:}-2=e^{-t}
integral of (y^2+14y+49)/((y^2+49)^2)	\int\:\frac{y^{2}+14y+49}{(y^{2}+49)^{2}}dy
y^'+(1+3x^2)y=3+9x^2	y^{\prime\:}+(1+3x^{2})y=3+9x^{2}
integral of (1+2t^3)/t	\int\:\frac{1+2t^{3}}{t}dt
(\partial)/(\partial x)(2e^{2x})	\frac{\partial\:}{\partial\:x}(2e^{2x})
derivative of f(x)=sqrt(x)(x^3+2x+3)	derivative\:f(x)=\sqrt{x}(x^{3}+2x+3)
y^{''}=a^2y	y^{\prime\:\prime\:}=a^{2}y
integral of (18)/(x(x^2+4)^2)	\int\:\frac{18}{x(x^{2}+4)^{2}}dx
area 4-x,-2,6	area\:4-x,-2,6
integral of (e^{3x})/(1+e^{3x)}	\int\:\frac{e^{3x}}{1+e^{3x}}dx
derivative of (-x^2+4/((x^2+4)^2))	\frac{d}{dx}(\frac{-x^{2}+4}{(x^{2}+4)^{2}})
integral of 2t^5	\int\:2t^{5}dt
y^'=-y/2	y^{\prime\:}=-\frac{y}{2}
y^{''}-8y^'=-2x-1	y^{\prime\:\prime\:}-8y^{\prime\:}=-2x-1
derivative of 2x^3-3x^2+x-1	derivative\:2x^{3}-3x^{2}+x-1
inverse oflaplace s/(s^2-2s+3)	inverselaplace\:\frac{s}{s^{2}-2s+3}
(\partial)/(\partial x)(4x^2)	\frac{\partial\:}{\partial\:x}(4x^{2})
integral of sqrt(4+9x^2)	\int\:\sqrt{4+9x^{2}}dx
integral of sin(3x)cos(4x)sin(2x)	\int\:\sin(3x)\cos(4x)\sin(2x)dx
derivative of (x*cos(x+pi)/(x-pi))	\frac{d}{dx}(\frac{x\cdot\:\cos(x)+π}{x-π})
derivative of r/(sqrt(r^2+7))	derivative\:\frac{r}{\sqrt{r^{2}+7}}
derivative of f(x)=(4x^3+2x+5)/x	derivative\:f(x)=\frac{4x^{3}+2x+5}{x}
derivative of f(x)= 5/((x+2)^2)	derivative\:f(x)=\frac{5}{(x+2)^{2}}
derivative of 9(x^3-x^4)	\frac{d}{dx}(9(x^{3}-x)^{4})
integral of x/((x^2+a^2)^{3/2)}	\int\:\frac{x}{(x^{2}+a^{2})^{\frac{3}{2}}}dx
y^{''}-6y^'+12y=sin(2x)	y^{\prime\:\prime\:}-6y^{\prime\:}+12y=\sin(2x)
y^{''}+y=e^{-x}	y^{\prime\:\prime\:}+y=e^{-x}
tangent of y=sqrt(x)(49.7)	tangent\:y=\sqrt{x}(49.7)
integral of 1/(e^{-2x)}	\int\:\frac{1}{e^{-2x}}dx
integral of 2x^2sin(pix)	\int\:2x^{2}\sin(πx)dx
integral of (y^4+2y^2)/(sqrt(y))	\int\:\frac{y^{4}+2y^{2}}{\sqrt{y}}dy
derivative of f(x)=arccsc(3x)	derivative\:f(x)=\arccsc(3x)
(\partial)/(\partial x)(sin(4x^3y-5xy^4))	\frac{\partial\:}{\partial\:x}(\sin(4x^{3}y-5xy^{4}))
limit as x approaches 4 of 7^x+12x	\lim\:_{x\to\:4}(7^{x}+12x)
integral of x^3(a^2+x^2)^{1/2}	\int\:x^{3}(a^{2}+x^{2})^{\frac{1}{2}}dx
derivative of y=6^x	derivative\:y=6^{x}
tangent of y=sqrt(7x),(7,7)	tangent\:y=\sqrt{7x},(7,7)
integral of x/(sqrt(3x^2+4))	\int\:\frac{x}{\sqrt{3x^{2}+4}}dx
tangent of f(x)= x/(2x-4),\at x=5	tangent\:f(x)=\frac{x}{2x-4},\at\:x=5
sum from n=1 to infinity of 2/(1+n^2)	\sum\:_{n=1}^{\infty\:}\frac{2}{1+n^{2}}
derivative of-2x+4	\frac{d}{dx}(-2x+4)
derivative of 1/(2sqrt(x+3))	derivative\:\frac{1}{2\sqrt{x+3}}
derivative of 2+sec(x)	\frac{d}{dx}(2+\sec(x))
laplacetransform 1/4	laplacetransform\:\frac{1}{4}
derivative of arctan(3x^2)	\frac{d}{dx}(\arctan(3x^{2}))
integral from 0 to infinity of xe^{-bx}	\int\:_{0}^{\infty\:}xe^{-bx}dx
tangent of y=(sqrt(x))/(x+6),(4,0.2)	tangent\:y=\frac{\sqrt{x}}{x+6},(4,0.2)
integral of x^2(x^3-11)^6	\int\:x^{2}(x^{3}-11)^{6}dx
sum from n=1 to infinity of 1/(1+2^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{1+2^{n}}
maclaurin ln(1+x^5)	maclaurin\:\ln(1+x^{5})
integral of x^2sqrt(11+x^3)	\int\:x^{2}\sqrt{11+x^{3}}dx
f(x)=tan(3x)	f(x)=\tan(3x)
derivative of-0.9x^2+1.7x+2.5	\frac{d}{dx}(-0.9x^{2}+1.7x+2.5)
integral of x^3arcsin(1/x)	\int\:x^{3}\arcsin(\frac{1}{x})dx
(\partial)/(\partial x)(y^3-x^2y)	\frac{\partial\:}{\partial\:x}(y^{3}-x^{2}y)
derivative of f(x)=8x^9-3x^6+12x^3	derivative\:f(x)=8x^{9}-3x^{6}+12x^{3}
area y=4x-x^2,y=0	area\:y=4x-x^{2},y=0
derivative of (X-1)e^X	derivative\:(X-1)e^{X}
implicit (dy)/(dx),4y^2+2=3x^2	implicit\:\frac{dy}{dx},4y^{2}+2=3x^{2}
integral of (-1)/(x^2)	\int\:\frac{-1}{x^{2}}dx
integral of 1/(sqrt(x^2+2x+101))	\int\:\frac{1}{\sqrt{x^{2}+2x+101}}dx
limit as x approaches 0 of (x^2+4x-2)/x	\lim\:_{x\to\:0}(\frac{x^{2}+4x-2}{x})
laplacetransform e^{-2t}sin(2t)	laplacetransform\:e^{-2t}\sin(2t)
integral of (-5/x+e^{-2x})	\int\:(-\frac{5}{x}+e^{-2x})dx

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