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Popular Calculus Problems

integral of-2x+12x^2-4x^3+14	\int\:-2x+12x^{2}-4x^{3}+14dx
integral of (2sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{2\sin^{3}(\sqrt{x})}{\sqrt{x}}dx
integral of (44-x)/(x^2+2x-24)	\int\:\frac{44-x}{x^{2}+2x-24}dx
integral of (2x^2+3x+2)/((x^2+1)^2)	\int\:\frac{2x^{2}+3x+2}{(x^{2}+1)^{2}}dx
laplacetransform 1+e^{4t}	laplacetransform\:1+e^{4t}
limit as x approaches-4 of 8x+3	\lim\:_{x\to\:-4}(8x+3)
y^'+y=te^t	y^{\prime\:}+y=te^{t}
x(dy)/(dx)+4y=2-7/x	x\frac{dy}{dx}+4y=2-\frac{7}{x}
integral of (x^3+4x-3)	\int\:(x^{3}+4x-3)dx
derivative of 5x^{-15}	derivative\:5x^{-15}
integral of (10x+15)/(x^2+3x)	\int\:\frac{10x+15}{x^{2}+3x}dx
(dy)/(dx)=(2-x)/(y-3)	\frac{dy}{dx}=\frac{2-x}{y-3}
integral of 1/(x(x-1)(x-2))	\int\:\frac{1}{x(x-1)(x-2)}dx
(\partial)/(\partial v)(sqrt(v/u))	\frac{\partial\:}{\partial\:v}(\sqrt{\frac{v}{u}})
derivative of f(x)=(2x)^{4x}	derivative\:f(x)=(2x)^{4x}
y^{''}+16y=2sin(2t)	y^{\prime\:\prime\:}+16y=2\sin(2t)
derivative of sqrt(x^2-5)	\frac{d}{dx}(\sqrt{x^{2}-5})
integral of-13cos^3(x)sin(x)	\int\:-13\cos^{3}(x)\sin(x)dx
integral from 0 to 1 of 5/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{5}{\sqrt{x}(x+1)}dx
(2xy+2x^3y)dx-(1+x^2)dy=0	(2xy+2x^{3}y)dx-(1+x^{2})dy=0
limit as x approaches infinity of ax^4+bx^2+c	\lim\:_{x\to\:\infty\:}(ax^{4}+bx^{2}+c)
limit as x approaches 0 of (3x-1)/(2x)	\lim\:_{x\to\:0}(\frac{3x-1}{2x})
integral from 0 to 1 of (ln(x))/x	\int\:_{0}^{1}\frac{\ln(x)}{x}dx
(\partial)/(\partial x)(scos(t))	\frac{\partial\:}{\partial\:x}(s\cos(t))
integral of 1/(x^4sqrt(x^2-3))	\int\:\frac{1}{x^{4}\sqrt{x^{2}-3}}dx
d/(du)(arctan(u/v))	\frac{d}{du}(\arctan(\frac{u}{v}))
derivative of 2cos(4x)	\frac{d}{dx}(2\cos(4x))
taylor (x^2+1)*e^{x-1},1	taylor\:(x^{2}+1)\cdot\:e^{x-1},1
integral of 11tan^4(x)sec^6(x)	\int\:11\tan^{4}(x)\sec^{6}(x)dx
integral of e^xsqrt(e^{2x)-1}	\int\:e^{x}\sqrt{e^{2x}-1}dx
integral of (x^6)/((6+x^7)^2)	\int\:\frac{x^{6}}{(6+x^{7})^{2}}dx
derivative of (5+3/x ^3)	\frac{d}{dx}((5+\frac{3}{x})^{3})
derivative of (1+q^{-1})^2	derivative\:(1+q^{-1})^{2}
(\partial)/(\partial x)(e^y+x+x^2+9)	\frac{\partial\:}{\partial\:x}(e^{y}+x+x^{2}+9)
integral of ((4x)/y)	\int\:(\frac{4x}{y})dx
(dy)/(dx)=x-y	\frac{dy}{dx}=x-y
area 16-x^2,x^2-2	area\:16-x^{2},x^{2}-2
integral of 4-4/(x^2)	\int\:4-\frac{4}{x^{2}}dx
limit as x approaches 0 of (7sin(x))/x	\lim\:_{x\to\:0}(\frac{7\sin(x)}{x})
derivative of (4x)/(3-tan(x))	derivative\:\frac{4x}{3-\tan(x)}
integral of cos(θ)	\int\:\cos(θ)dθ
(\partial)/(\partial y)(xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:y}(xye^{-x^{2}-y^{2}})
integral from 0 to 1 of 7/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{7}{\sqrt{x}(x+1)}dx
integral from 3 to 5 of 1/(x-4)	\int\:_{3}^{5}\frac{1}{x-4}dx
derivative of y=(x^2-4x)^5	derivative\:y=(x^{2}-4x)^{5}
integral from 1 to infinity of e^{-x}	\int\:_{1}^{\infty\:}e^{-x}dx
(x^{x^{x^x}})^'	(x^{x^{x^{x}}})^{\prime\:}
(7x+6y)dx+(6x-8y3)dy=0	(7x+6y)dx+(6x-8y3)dy=0
limit as x approaches 0 of (sin(7x))/x	\lim\:_{x\to\:0}(\frac{\sin(7x)}{x})
derivative of 1-tan(x)	\frac{d}{dx}(1-\tan(x))
(d^2)/(dx^2)(cos^2(4pix))	\frac{d^{2}}{dx^{2}}(\cos^{2}(4πx))
y^{'''}-y^{''}-y^'=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-y^{\prime\:}=0
integral of 7xe^{2x}	\int\:7xe^{2x}dx
limit as x approaches pi of (x+pi)csc(x)	\lim\:_{x\to\:π}((x+π)\csc(x))
derivative of f(x)=sqrt((z-5)/(z+5))	derivative\:f(x)=\sqrt{\frac{z-5}{z+5}}
integral of (x^3e^{x^2})/((x^2+1)^2)	\int\:\frac{x^{3}e^{x^{2}}}{(x^{2}+1)^{2}}dx
laplacetransform f(t)=te^{4t}	laplacetransform\:f(t)=te^{4t}
integral from-infinity to 0 of xe^{5x}	\int\:_{-\infty\:}^{0}xe^{5x}dx
tangent of y=sqrt(5x+11)	tangent\:y=\sqrt{5x+11}
sum from n=2 to infinity of (e^n)/(n!)	\sum\:_{n=2}^{\infty\:}\frac{e^{n}}{n!}
integral of 3/(x(x^4+4))	\int\:\frac{3}{x(x^{4}+4)}dx
derivative of xln(x/5)	\frac{d}{dx}(x\ln(\frac{x}{5}))
derivative of (1+x^x)	\frac{d}{dx}((1+x)^{x})
derivative of 1/2 bh	derivative\:\frac{1}{2}bh
y^'+x^{-1}y=2xy^2	y^{\prime\:}+x^{-1}y=2xy^{2}
limit as x approaches 25/9 of 3(x^2)/2	\lim\:_{x\to\:\frac{25}{9}}(3\frac{x^{2}}{2})
integral of (tan(x))/(cos(x))	\int\:\frac{\tan(x)}{\cos(x)}dx
limit as x approaches 4 of 9*27	\lim\:_{x\to\:4}(9\cdot\:27)
limit as x approaches-1 of x-ln(-x-1)	\lim\:_{x\to\:-1}(x-\ln(-x-1))
simplify arctan(y/x)	simplify\:\arctan(\frac{y}{x})
integral from 0 to 3 of \|3x-5\|	\int\:_{0}^{3}\left\|3x-5\right\|dx
derivative of 1-(3x/(x^3+27))	\frac{d}{dx}(1-\frac{3x}{x^{3}+27})
integral of (2-sqrt(t))/(t^2)	\int\:\frac{2-\sqrt{t}}{t^{2}}dt
limit as x approaches-infinity of ((x^2-5x))/(x-2)	\lim\:_{x\to\:-\infty\:}(\frac{(x^{2}-5x)}{x-2})
(dy)/(dx)=1-2x	\frac{dy}{dx}=1-2x
integral of xarctan(2x)	\int\:x\arctan(2x)dx
derivative of (1-cos(x)/(sin(x)))	\frac{d}{dx}(\frac{1-\cos(x)}{\sin(x)})
(\partial}{\partial x}(y+\frac{x^2)/y)	\frac{\partial\:}{\partial\:x}(y+\frac{x^{2}}{y})
derivative of 1/10 x^5-3/4 x^4+4/3 x^3	\frac{d}{dx}(\frac{1}{10}x^{5}-\frac{3}{4}x^{4}+\frac{4}{3}x^{3})
derivative of (x^2+1^3)	\frac{d}{dx}((x^{2}+1)^{3})
d/(da)(1+sin(a)+cos(a))	\frac{d}{da}(1+\sin(a)+\cos(a))
derivative of (100(x+25)/x)	\frac{d}{dx}(\frac{100(x+25)}{x})
integral of (6x-12)/(x^2)	\int\:\frac{6x-12}{x^{2}}dx
inverse oflaplace (50000)/(s^2)	inverselaplace\:\frac{50000}{s^{2}}
integral from 0 to 1 of (x^2)/(x+1)	\int\:_{0}^{1}\frac{x^{2}}{x+1}dx
xy^2dx=dy-xdx,y(0)=-1	xy^{2}dx=dy-xdx,y(0)=-1
(dx)/(dy)	\frac{dx}{dy}
integral of (x^2)/(sqrt(1-x))	\int\:\frac{x^{2}}{\sqrt{1-x}}dx
θ^{''}+(4k)/3 θ=0	θ^{\prime\:\prime\:}+\frac{4k}{3}θ=0
derivative of (e^x(x^2+2x^3)/(3x^2+x))	\frac{d}{dx}(\frac{e^{x}(x^{2}+2x)^{3}}{3x^{2}+x})
area y= 4/(x^2+4),[-10,10]	area\:y=\frac{4}{x^{2}+4},[-10,10]
derivative of (x-y^2)	\frac{d}{dx}((x-y)^{2})
derivative of sqrt(4x-17)	derivative\:\sqrt{4x-17}
integral of (cos^2(4x))/4	\int\:\frac{\cos^{2}(4x)}{4}dx
inverse oflaplace 1/s*((10)/(s^2+s+10))	inverselaplace\:\frac{1}{s}\cdot\:(\frac{10}{s^{2}+s+10})
laplacetransform-4e^{3t}	laplacetransform\:-4e^{3t}
limit as x approaches 0 of-9x^2+6x	\lim\:_{x\to\:0}(-9x^{2}+6x)
derivative of csc(2x)	derivative\:\csc(2x)
derivative of f(t)=4t-9t^2	derivative\:f(t)=4t-9t^{2}
integral of (3x-4)x^2	\int\:(3x-4)x^{2}dx

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