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Popular Calculus Problems

integral of sin^6(x)cos(x)	\int\:\sin^{6}(x)\cos(x)dx
derivative of x^n	derivative\:x^{n}
integral of (x^4-9x)^2(4x^3-9)	\int\:(x^{4}-9x)^{2}(4x^{3}-9)dx
limit as x approaches 0 of (cot(pix)*sin(x))/(2sec(x))	\lim\:_{x\to\:0}(\frac{\cot(πx)\cdot\:\sin(x)}{2\sec(x)})
integral of sin(x)cos(kx)	\int\:\sin(x)\cos(kx)dx
integral of 9(9x+4)	\int\:9(9x+4)dx
derivative of f(x)=x^2-2cos(x)-3	derivative\:f(x)=x^{2}-2\cos(x)-3
xy^2y^'=y^3-x^3	xy^{2}y^{\prime\:}=y^{3}-x^{3}
integral of ((1))/(25x^2-16)	\int\:\frac{(1)}{25x^{2}-16}dx
(dy)/(dx)+6y=e^x	\frac{dy}{dx}+6y=e^{x}
integral of x^3+x^{1/3}	\int\:x^{3}+x^{\frac{1}{3}}dx
integral of 5sin^3(2xco)s^32x	\int\:5\sin^{3}(2xco)s^{3}2xdx
y^{''}+4y=4sin(2t)	y^{\prime\:\prime\:}+4y=4\sin(2t)
derivative of y= 2/3 x^3-3/(4x^2)	derivative\:y=\frac{2}{3}x^{3}-\frac{3}{4x^{2}}
(\partial)/(\partial y)((cos(y))/(xz^2))	\frac{\partial\:}{\partial\:y}(\frac{\cos(y)}{xz^{2}})
y^{'''}=6	y^{\prime\:\prime\:\prime\:}=6
integral of sin(3pit)	\int\:\sin(3πt)dt
integral of 1/(5-2x)	\int\:\frac{1}{5-2x}dx
derivative of tsin(x)	\frac{d}{dx}(t\sin(x))
(\partial)/(\partial x)(x^2+y^2+xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+xy)
derivative of f(x)=2cos(2x)	derivative\:f(x)=2\cos(2x)
(2x+3y)dx+(6x+9y-3)dy=0	(2x+3y)dx+(6x+9y-3)dy=0
(\partial)/(\partial y)(y^3+2ye^x)	\frac{\partial\:}{\partial\:y}(y^{3}+2ye^{x})
(\partial)/(\partial x)(2x^3y+cos(x^3))	\frac{\partial\:}{\partial\:x}(2x^{3}y+\cos(x^{3}))
(\partial)/(\partial y)((100)/(5x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{100}{5x^{2}+y^{2}})
inverse oflaplace s/(s^2+4s)	inverselaplace\:\frac{s}{s^{2}+4s}
integral of (x^3+4)/(x^2)	\int\:\frac{x^{3}+4}{x^{2}}dx
(\partial)/(\partial x)(5x^5y^8+8x^6y^7)	\frac{\partial\:}{\partial\:x}(5x^{5}y^{8}+8x^{6}y^{7})
integral from 0 to infinity of x/(1+x^4)	\int\:_{0}^{\infty\:}\frac{x}{1+x^{4}}dx
integral of e^{(2x)/pi}	\int\:e^{\frac{2x}{π}}dx
integral of ((x+1))/(x^2+5x+6)	\int\:\frac{(x+1)}{x^{2}+5x+6}dx
derivative of 1-3x	derivative\:1-3x
integral of (tan(ln(2x+4)))/(2x+4)	\int\:\frac{\tan(\ln(2x+4))}{2x+4}dx
taylor sqrt(4x+1)	taylor\:\sqrt{4x+1}
derivative of 1-x^{3/2}	\frac{d}{dx}(1-x^{\frac{3}{2}})
integral of (2x+3)^3	\int\:(2x+3)^{3}dx
derivative of (25x^3/3+10x^2+4x-7)	\frac{d}{dx}(\frac{25x^{3}}{3}+10x^{2}+4x-7)
f^'(x)=e^{-2x}	f^{\prime\:}(x)=e^{-2x}
derivative of (2x+sin(x)/(2x+cos(x)))	\frac{d}{dx}(\frac{2x+\sin(x)}{2x+\cos(x)})
slope of (1,10),(24,-26)	slope\:(1,10),(24,-26)
limit as x approaches 4-of 5-x	\lim\:_{x\to\:4-}(5-x)
(\partial)/(\partial x)(1/i+1/o)	\frac{\partial\:}{\partial\:x}(\frac{1}{i}+\frac{1}{o})
integral from 0 to 2 of (2-x)	\int\:_{0}^{2}(2-x)dx
limit as x approaches 1 of cos(x)	\lim\:_{x\to\:1}(\cos(x))
(dy)/(dx)=(y-1-2y+y+1)/(x^2)	\frac{dy}{dx}=\frac{y-1-2y+y+1}{x^{2}}
area y=(-x^3)/2-(x^2)/2+(5x)/2 ,y=(-x)/2	area\:y=\frac{-x^{3}}{2}-\frac{x^{2}}{2}+\frac{5x}{2},y=\frac{-x}{2}
integral of (-2e^{3x}+5/x)	\int\:(-2e^{3x}+\frac{5}{x})dx
limit as x approaches+1 of ln(x)	\lim\:_{x\to\:+1}(\ln(x))
integral of (4x^3-5x^2)/((x-2)(x+1))	\int\:\frac{4x^{3}-5x^{2}}{(x-2)(x+1)}dx
area 6x, 2/3 x,40-x^2	area\:6x,\frac{2}{3}x,40-x^{2}
derivative of 6cos(xsin(x))	\frac{d}{dx}(6\cos(x)\sin(x))
(\partial)/(\partial x)(e^{5y})	\frac{\partial\:}{\partial\:x}(e^{5y})
integral of 1/(x^2*sqrt(4-x^2))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{4-x^{2}}}dx
limit as x approaches 0-of 5/x-5/(\|x\|)	\lim\:_{x\to\:0-}(\frac{5}{x}-\frac{5}{\left\|x\right\|})
limit as x approaches-2-of 2x+sqrt(2+x)	\lim\:_{x\to\:-2-}(2x+\sqrt{2+x})
taylor ln(1-4y)	taylor\:\ln(1-4y)
(\partial)/(\partial x)(cos(8x)sin(4y))	\frac{\partial\:}{\partial\:x}(\cos(8x)\sin(4y))
derivative of 1/((2x^3+3x+5)^{3/4)}	derivative\:\frac{1}{(2x^{3}+3x+5)^{\frac{3}{4}}}
integral from 1 to e of (ln(x))^2	\int\:_{1}^{e}(\ln(x))^{2}dx
integral of (x^2)/(x^3+1)	\int\:\frac{x^{2}}{x^{3}+1}dx
(dy}{dx}=\frac{(-xe^{-x^2}))/y	\frac{dy}{dx}=\frac{(-xe^{-x^{2}})}{y}
integral of 8x^2cos(2x)	\int\:8x^{2}\cos(2x)dx
integral of (x^2+1)^3*x	\int\:(x^{2}+1)^{3}\cdot\:xdx
sum from n=1 to infinity of (1/n)(1/n)^2	\sum\:_{n=1}^{\infty\:}(\frac{1}{n})(\frac{1}{n})^{2}
y^'=(2xy)/(x^2+1)	y^{\prime\:}=\frac{2xy}{x^{2}+1}
tangent of f(x)=6+sqrt(1-x),\at x=-8	tangent\:f(x)=6+\sqrt{1-x},\at\:x=-8
integral of (x-8)/((x+4)^2+64)	\int\:\frac{x-8}{(x+4)^{2}+64}dx
d/(dt)(e^{-4t})	\frac{d}{dt}(e^{-4t})
x(dy)/(dx)+3x^2+4y=0	x\frac{dy}{dx}+3x^{2}+4y=0
derivative of x*e^x	derivative\:x\cdot\:e^{x}
integral of (1/x)/(ln(x))	\int\:\frac{\frac{1}{x}}{\ln(x)}dx
derivative of (e^{-x})/(1+e^{-x)}	derivative\:\frac{e^{-x}}{1+e^{-x}}
derivative of 2(1-sin(x))	\frac{d}{dx}(2(1-\sin(x)))
integral of 8xe^{4x^2}	\int\:8xe^{4x^{2}}dx
taylor sin(x), pi/5	taylor\:\sin(x),\frac{π}{5}
derivative of f(x)=4^2	derivative\:f(x)=4^{2}
integral of ln(v)	\int\:\ln(v)dv
(\partial)/(\partial x)(e^{-x^3})	\frac{\partial\:}{\partial\:x}(e^{-x^{3}})
tangent of f(x)= 3/(sqrt(x))	tangent\:f(x)=\frac{3}{\sqrt{x}}
(\partial)/(\partial y)(6x^{1/3}y^{2/3})	\frac{\partial\:}{\partial\:y}(6x^{\frac{1}{3}}y^{\frac{2}{3}})
(\partial)/(\partial x)((4x)/((y+2z)^3))	\frac{\partial\:}{\partial\:x}(\frac{4x}{(y+2z)^{3}})
limit as x approaches 0 of 1/x sin(x)	\lim\:_{x\to\:0}(\frac{1}{x}\sin(x))
integral from 0 to 3pi of \|sin(x)\|	\int\:_{0}^{3π}\left\|\sin(x)\right\|dx
derivative of (2x/(x-3))	\frac{d}{dx}(\frac{2x}{x-3})
derivative of f(x)=(3+x)/(1-3x)	derivative\:f(x)=\frac{3+x}{1-3x}
integral of 1/(x^4-1)	\int\:\frac{1}{x^{4}-1}dx
limit as x approaches 2 of (2-x)/(4-x^2)	\lim\:_{x\to\:2}(\frac{2-x}{4-x^{2}})
d/(d{x)}({x}^3+2{x}{y}+{y}^2+{z}^2-5{x}-4{z})	\frac{d}{d{x}}({x}^{3}+2{x}{y}+{y}^{2}+{z}^{2}-5{x}-4{z})
limit as x approaches 9 of (81)/(9-x)	\lim\:_{x\to\:9}(\frac{81}{9-x})
tangent of x^2+4/x-10	tangent\:x^{2}+\frac{4}{x}-10
derivative of 3x-4x^2	derivative\:3x-4x^{2}
integral of (x^{1.8}+9x^{3.5})	\int\:(x^{1.8}+9x^{3.5})dx
y^{''}-y^'-2y=8e^{-t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=8e^{-t}
derivative of (-2^x)	\frac{d}{dx}((-2)^{x})
derivative of 4x^{-1}	derivative\:4x^{-1}
(\partial)/(\partial y)(x^2-4y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-4y^{2})
slope of (0,-2),(-1/2 ,3)	slope\:(0,-2),(-\frac{1}{2},3)
sum from n=5 to infinity of 1/(n(n+1))	\sum\:_{n=5}^{\infty\:}\frac{1}{n(n+1)}
(dy)/(dx)=sin(5x)	\frac{dy}{dx}=\sin(5x)
integral of 5x-1	\int\:5x-1dx

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