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Popular Calculus Problems

integral of sec(2x)tan^3(2x)	\int\:\sec(2x)\tan^{3}(2x)dx
maclaurin e^{(x^2)/2}	maclaurin\:e^{\frac{x^{2}}{2}}
integral from 0 to pi/8 of sin^2(2x)	\int\:_{0}^{\frac{π}{8}}\sin^{2}(2x)dx
taylor sin(x)cos(x)	taylor\:\sin(x)\cos(x)
integral of x^3(x^4+3)^2	\int\:x^{3}(x^{4}+3)^{2}dx
y=x^5-4x^3+2x-3	y=x^{5}-4x^{3}+2x-3
derivative of (8x)/(1-x)	derivative\:\frac{8x}{1-x}
laplacetransform-2t+8	laplacetransform\:-2t+8
derivative of (x^3/3-2x^2+3x)	\frac{d}{dx}(\frac{x^{3}}{3}-2x^{2}+3x)
derivative of-(2x/((9+x^2)^2))	\frac{d}{dx}(-\frac{2x}{(9+x^{2})^{2}})
(dx)/(dt)=12-x/(200+3t)	\frac{dx}{dt}=12-\frac{x}{200+3t}
tangent of f(x)=x^3-3x^2-9x+27,\at x=4	tangent\:f(x)=x^{3}-3x^{2}-9x+27,\at\:x=4
(\partial)/(\partial x)((3x+y^2)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{3x+y^{2}}{xy})
integral of (5x^4-8x^3+9x^2-2x+7)	\int\:(5x^{4}-8x^{3}+9x^{2}-2x+7)dx
y^'=y^5	y^{\prime\:}=y^{5}
derivative of (3x-5/(2x+3))	\frac{d}{dx}(\frac{3x-5}{2x+3})
limit as x approaches 0 of (sin(x/2))^x	\lim\:_{x\to\:0}((\sin(\frac{x}{2}))^{x})
integral of (x^2)/(x^3)	\int\:\frac{x^{2}}{x^{3}}dx
integral of 4^t	\int\:4^{t}dt
d/(dy)(x^y)	\frac{d}{dy}(x^{y})
(\partial)/(\partial x)(e^x+y^2)	\frac{\partial\:}{\partial\:x}(e^{x}+y^{2})
derivative of (cos(9x)^x)	\frac{d}{dx}((\cos(9x))^{x})
integral of (sqrt(x+1)-1)/(sqrt(x+1)+1)	\int\:\frac{\sqrt{x+1}-1}{\sqrt{x+1}+1}dx
derivative of y=19^x	derivative\:y=19^{x}
integral of (2y)/(y^2+1)	\int\:\frac{2y}{y^{2}+1}dy
limit as x approaches 0-of 2/3 x^{-1/3}	\lim\:_{x\to\:0-}(\frac{2}{3}x^{-\frac{1}{3}})
integral from 0 to infinity of e^{-14x}	\int\:_{0}^{\infty\:}e^{-14x}dx
(d^3)/(dx^3)((1-5x)/(1+5x))	\frac{d^{3}}{dx^{3}}(\frac{1-5x}{1+5x})
limit as x approaches-3 of 14	\lim\:_{x\to\:-3}(14)
tangent of f(x)=x^2+8,(2,12)	tangent\:f(x)=x^{2}+8,(2,12)
integral of 3x^{2/3}	\int\:3x^{\frac{2}{3}}dx
derivative of-3/(x^3)	derivative\:-\frac{3}{x^{3}}
integral of (()/1)^2	\int\:(\frac{dy}{1})^{2}dx
(\partial)/(\partial x)(e^{-x-y})	\frac{\partial\:}{\partial\:x}(e^{-x-y})
(\partial)/(\partial y)(x^2yz^2+sin(yz))	\frac{\partial\:}{\partial\:y}(x^{2}yz^{2}+\sin(yz))
(dx)/(dt)=x-x^2	\frac{dx}{dt}=x-x^{2}
derivative of 4^{3x}	\frac{d}{dx}(4^{3x})
integral of (6x+4)/(x^2(x^2+2))	\int\:\frac{6x+4}{x^{2}(x^{2}+2)}dx
(x-2y)dy+(y+4x)dx=0	(x-2y)dy+(y+4x)dx=0
derivative of 3x^4sqrt(25-x^2)	derivative\:3x^{4}\sqrt{25-x^{2}}
integral of 4sin(t)cos(t)	\int\:4\sin(t)\cos(t)dt
limit as x approaches 3 of (x^3-27)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{3}-27}{x-3})
(dy)/(dx)=(3sec(y))/((x-4)^2)	\frac{dy}{dx}=\frac{3\sec(y)}{(x-4)^{2}}
integral of (2x^5-sqrt(x))/x	\int\:\frac{2x^{5}-\sqrt{x}}{x}dx
(dy)/(dx)=((y^2+6))/(2y)	\frac{dy}{dx}=\frac{(y^{2}+6)}{2y}
derivative of cos(x+sin(y))	\frac{d}{dx}(\cos(x)+\sin(y))
inverse oflaplace 1/(s(s+4)(s+2))	inverselaplace\:\frac{1}{s(s+4)(s+2)}
integral of (ln(3x+1))/(12x+4)	\int\:\frac{\ln(3x+1)}{12x+4}dx
(d^2)/(dx^2)(x(x-4)^3)	\frac{d^{2}}{dx^{2}}(x(x-4)^{3})
derivative of e^{ax}	derivative\:e^{ax}
integral of 5x^5-x	\int\:5x^{5}-xdx
integral of sec^9(x)	\int\:\sec^{9}(x)dx
integral from 0 to 1 of ln(t)	\int\:_{0}^{1}\ln(t)dt
(\partial)/(\partial x)(2x^{1/2}+y)	\frac{\partial\:}{\partial\:x}(2x^{\frac{1}{2}}+y)
derivative of f(x)=sqrt(9x+7)	derivative\:f(x)=\sqrt{9x+7}
integral of 3/(6+3x)	\int\:\frac{3}{6+3x}dx
integral of 2/(npi)sin((npix)/2)	\int\:\frac{2}{nπ}\sin(\frac{nπx}{2})dx
derivative of x/(7+x^2)	\frac{d}{dx}(\frac{x}{7+x^{2}})
integral of (cot(x))^2	\int\:(\cot(x))^{2}dx
integral of x^2*e^{x^3}	\int\:x^{2}\cdot\:e^{x^{3}}dx
derivative of-(2x^3/y)	\frac{d}{dx}(-\frac{2x^{3}}{y})
integral of y/((y+2)(4y-1))	\int\:\frac{y}{(y+2)(4y-1)}dy
tangent of y=4.5x^2-3x+2	tangent\:y=4.5x^{2}-3x+2
(\partial)/(\partial x)(e^{x/2})	\frac{\partial\:}{\partial\:x}(e^{\frac{x}{2}})
y^'=sec^2(x)(1-3y),y(pi/4)=0	y^{\prime\:}=\sec^{2}(x)(1-3y),y(\frac{π}{4})=0
tangent of f(x)=sqrt(x^2+16),\at x=3	tangent\:f(x)=\sqrt{x^{2}+16},\at\:x=3
integral of sin^3(5x)cot(5x)	\int\:\sin^{3}(5x)\cot(5x)dx
6y^{''}+9y^'=0	6y^{\prime\:\prime\:}+9y^{\prime\:}=0
integral of 1/((x^2-2x+1)sqrt(x^2-2x))	\int\:\frac{1}{(x^{2}-2x+1)\sqrt{x^{2}-2x}}dx
(\partial)/(\partial z)(2x^2y)	\frac{\partial\:}{\partial\:z}(2x^{2}y)
derivative of 2x^5+6x^8	\frac{d}{dx}(2x^{5}+6x^{8})
integral from 0 to 1 of (7x+sqrt(x))	\int\:_{0}^{1}(7x+\sqrt{x})dx
derivative of f(x)=x^5+5^x	derivative\:f(x)=x^{5}+5^{x}
derivative of f(x)=-4sqrt(6x^2-5x+10)	derivative\:f(x)=-4\sqrt{6x^{2}-5x+10}
limit as x approaches 0 of 3-x	\lim\:_{x\to\:0}(3-x)
(\partial)/(\partial θ)(acos(θ))	\frac{\partial\:}{\partial\:θ}(a\cos(θ))
(\partial)/(\partial x)(5x^2y+6xy^3)	\frac{\partial\:}{\partial\:x}(5x^{2}y+6xy^{3})
y^'=9y^2sin(x)	y^{\prime\:}=9y^{2}\sin(x)
tangent of f(x)=3x^3+5x^2+5x,\at x=-1	tangent\:f(x)=3x^{3}+5x^{2}+5x,\at\:x=-1
derivative of 2^x-2x	\frac{d}{dx}(2^{x}-2x)
area y=2x^2,y=2x+6,-2,2	area\:y=2x^{2},y=2x+6,-2,2
y(dy)/(dx)+8x^3=4x	y\frac{dy}{dx}+8x^{3}=4x
integral of tan(6x)	\int\:\tan(6x)dx
derivative of 2e^{x-5}	\frac{d}{dx}(2e^{x-5})
tangent of y=-9x^2	tangent\:y=-9x^{2}
sum from n=1 to infinity}((-1)^{n-1 of n^2)/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n-1}n^{2}}{10^{n}}
derivative of sqrt((x^2-3x/(2x+1)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-3x}{2x+1}})
derivative of sin(3x^4)	\frac{d}{dx}(\sin(3x^{4}))
derivative of 6sin(x-8e^x)	\frac{d}{dx}(6\sin(x)-8e^{x})
(d^2)/(dx^2)((1-5x)/(1+5x))	\frac{d^{2}}{dx^{2}}(\frac{1-5x}{1+5x})
tangent of f(x)=2x^2-5x,(-1,7)	tangent\:f(x)=2x^{2}-5x,(-1,7)
derivative of (x^2+3/(x^2+1))	\frac{d}{dx}(\frac{x^{2}+3}{x^{2}+1})
derivative of a^2+bx+c	\frac{d}{dx}(a^{2}+bx+c)
derivative of (2x+3/(x+4))	\frac{d}{dx}(\frac{2x+3}{x+4})
limit as x approaches 4 of (x-4)/(x-4)	\lim\:_{x\to\:4}(\frac{x-4}{x-4})
derivative of y=sqrt(5x+6)	derivative\:y=\sqrt{5x+6}
derivative of (e^x+e^{-x}/3)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{3})
derivative of (\|x-1\|/(\|x-3\|))	\frac{d}{dx}(\frac{\left\|x-1\right\|}{\left\|x-3\right\|})
taylor xln(x)	taylor\:x\ln(x)
derivative of f(x)=(x-3)/(5x+2)	derivative\:f(x)=\frac{x-3}{5x+2}

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