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Popular Calculus Problems

xy^'+y+4=0	xy^{\prime\:}+y+4=0
(\partial)/(\partial x)(2xe^{4xy})	\frac{\partial\:}{\partial\:x}(2xe^{4xy})
integral of x^3(4-x^2)^{1/4}	\int\:x^{3}(4-x^{2})^{\frac{1}{4}}dx
integral from 0 to 1 of x^2(x+1)^6	\int\:_{0}^{1}x^{2}(x+1)^{6}dx
inverse oflaplace 6/(s(s+3))	inverselaplace\:\frac{6}{s(s+3)}
derivative of 1/(1+5x)	\frac{d}{dx}(\frac{1}{1+5x})
derivative of asin^3(x)	\frac{d}{dx}(a\sin^{3}(x))
limit as x approaches 0-of (14x^3+15x)/x	\lim\:_{x\to\:0-}(\frac{14x^{3}+15x}{x})
maclaurin ln(1/3 (2+e^{-3x}))	maclaurin\:\ln(\frac{1}{3}(2+e^{-3x}))
y^{''}-4y+4y=e^{-t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-4y+4y=e^{-t},y(0)=0,y^{\prime\:}(0)=0
limit as x approaches+0 of 3^x+7	\lim\:_{x\to\:+0}(3^{x}+7)
derivative of ((t^3)/(t^8+9))^2	derivative\:(\frac{t^{3}}{t^{8}+9})^{2}
integral from 0.5 to 1 of 1.5x^2	\int\:_{0.5}^{1}1.5x^{2}dx
integral of (7x+4y)	\int\:(7x+4y)dy
derivative of ((x^4+1)/(x^2-1))	\frac{d}{dx}(\frac{(x^{4}+1)}{x^{2}-1})
area 3/x ,12x, 1/12 x	area\:\frac{3}{x},12x,\frac{1}{12}x
derivative of x^3(1-x^{100}+x^4-5pi)	\frac{d}{dx}(x^{3}(1-x)^{100}+x^{4}-5π)
y^'+7y=0	y^{\prime\:}+7y=0
limit as x approaches 5 of 5/((x-2)^2)	\lim\:_{x\to\:5}(\frac{5}{(x-2)^{2}})
(x^2+xy+y^2)dx=(x^2+xy)dy	(x^{2}+xy+y^{2})dx=(x^{2}+xy)dy
integral of sin^4(2θ)	\int\:\sin^{4}(2θ)dθ
(\partial)/(\partial y)(xsin(y-z))	\frac{\partial\:}{\partial\:y}(x\sin(y-z))
limit as x approaches 2 of (f(x))^3	\lim\:_{x\to\:2}((f(x))^{3})
integral of-(x^2)/2	\int\:-\frac{x^{2}}{2}dx
derivative of 3sin(x-x)	\frac{d}{dx}(3\sin(x)-x)
(\partial)/(\partial x)(3x^2+3y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}+3y^{2})
integral of (-5)	\int\:(-5)dx
integral of t/((t^2+1)^{25/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{25}{2}}}dt
area x^3+6x^2+8x,[-4,0]	area\:x^{3}+6x^{2}+8x,[-4,0]
(\partial)/(\partial x)(-x^3-y^2+3x^2-10y-6)	\frac{\partial\:}{\partial\:x}(-x^{3}-y^{2}+3x^{2}-10y-6)
integral of 1/((2-x))	\int\:\frac{1}{(2-x)}dx
integral of 1/(sqrt(3+x-x^2))	\int\:\frac{1}{\sqrt{3+x-x^{2}}}dx
derivative of (x^3-2x+1)(3x^3+2x^2-5x)	derivative\:(x^{3}-2x+1)(3x^{3}+2x^{2}-5x)
derivative of y=((x+1)^2)/(sqrt(x)+1)	derivative\:y=\frac{(x+1)^{2}}{\sqrt{x}+1}
((3y^2-t^2))/(y^5)dy+t/(2y^4)dt=0	\frac{(3y^{2}-t^{2})}{y^{5}}dy+\frac{t}{2y^{4}}dt=0
sum from n=0 to infinity of (3/5)^n	\sum\:_{n=0}^{\infty\:}(\frac{3}{5})^{n}
limit as x approaches+3-of 3/(x-3)	\lim\:_{x\to\:+3-}(\frac{3}{x-3})
integral of x*2^x	\int\:x\cdot\:2^{x}dx
integral of 4cos(4x)	\int\:4\cos(4x)dx
derivative of y=cos^7(pit-16)	derivative\:y=\cos^{7}(πt-16)
derivative of sqrt(x^5+4x^2-1)	\frac{d}{dx}(\sqrt{x^{5}+4x^{2}-1})
sum from k=2 to infinity of 1/(k(ln(k)))	\sum\:_{k=2}^{\infty\:}\frac{1}{k(\ln(k))}
derivative of-6sqrt(x)	derivative\:-6\sqrt{x}
d/(dy)(y^2e^{xy})	\frac{d}{dy}(y^{2}e^{xy})
derivative of xcsc(x-cot(x))	\frac{d}{dx}(x\csc(x)-\cot(x))
sum from n=0 to infinity of 6/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{6}{2^{n}}
derivative of f(x)=(-6)/x	derivative\:f(x)=\frac{-6}{x}
(\partial)/(\partial x)(-8xy-2x^4-2y^4)	\frac{\partial\:}{\partial\:x}(-8xy-2x^{4}-2y^{4})
limit as x approaches 0 of (6^x-5^x)/x	\lim\:_{x\to\:0}(\frac{6^{x}-5^{x}}{x})
derivative of f(x)=(x-3)/(x+3)	derivative\:f(x)=\frac{x-3}{x+3}
(\partial)/(\partial y)(x/(5+y))	\frac{\partial\:}{\partial\:y}(\frac{x}{5+y})
limit as x approaches-1 of x-1	\lim\:_{x\to\:-1}(x-1)
(d^2)/(dt^2)x+5 d/(dt)x+2x=0	\frac{d^{2}}{dt^{2}}x+5\frac{d}{dt}x+2x=0
(\partial)/(\partial y)(ln(x^3+y^2)-ln(xy))	\frac{\partial\:}{\partial\:y}(\ln(x^{3}+y^{2})-\ln(xy))
limit as x approaches 0 of (7^x-2^x)/x	\lim\:_{x\to\:0}(\frac{7^{x}-2^{x}}{x})
(dy)/(dx)+2xy+xy^4=0	\frac{dy}{dx}+2xy+xy^{4}=0
y^'+(6x+1/x)y=1	y^{\prime\:}+(6x+\frac{1}{x})y=1
x(dy)/(dx)+4y=5	x\frac{dy}{dx}+4y=5
integral of 6xe^{3x^2}	\int\:6xe^{3x^{2}}dx
ay^{''}+by^'=0	ay^{\prime\:\prime\:}+by^{\prime\:}=0
(dy}{dx}+\frac{2y)/x =2xy^{3/2}	\frac{dy}{dx}+\frac{2y}{x}=2xy^{\frac{3}{2}}
integral from 1 to 2 of x-1	\int\:_{1}^{2}x-1dx
derivative of f(x)=6sqrt(6x^{10)+7x^6}	derivative\:f(x)=6\sqrt{6x^{10}+7x^{6}}
slope of (0,-10),(5,-6)	slope\:(0,-10),(5,-6)
derivative of arcsinh(cot(x))	\frac{d}{dx}(\arcsinh(\cot(x)))
(\partial)/(\partial x)(ycos(z))	\frac{\partial\:}{\partial\:x}(y\cos(z))
integral of (xarccos(x))/(sqrt(1-x^2))	\int\:\frac{x\arccos(x)}{\sqrt{1-x^{2}}}dx
x^2y^{''}+6xy^'+6y=0	x^{2}y^{\prime\:\prime\:}+6xy^{\prime\:}+6y=0
integral from 1 to infinity of e^{-x}	\int\:_{1}^{\infty\:}e^{-x}dx
(\partial)/(\partial y)(y^2-cos(x)y)	\frac{\partial\:}{\partial\:y}(y^{2}-\cos(x)y)
derivative of (x^3/3+3/(x^3))	\frac{d}{dx}(\frac{x^{3}}{3}+\frac{3}{x^{3}})
derivative of \|x\|+\|x-1\|	\frac{d}{dx}(\left\|x\right\|+\left\|x-1\right\|)
derivative of xtan(2sqrt(x))	\frac{d}{dx}(x\tan(2\sqrt{x}))
(\partial)/(\partial x)(sin(x^3))	\frac{\partial\:}{\partial\:x}(\sin(x^{3}))
limit as x approaches 3+of (2x+1)/(x-3)	\lim\:_{x\to\:3+}(\frac{2x+1}{x-3})
integral of sin(4pit)	\int\:\sin(4πt)dt
integral of sqrt(2t^4+2)	\int\:\sqrt{2t^{4}+2}dt
integral of cos^2(x)sin(2x)	\int\:\cos^{2}(x)\sin(2x)dx
area 1-x^2,0	area\:1-x^{2},0
derivative of 4x^3-6x^2-72x	\frac{d}{dx}(4x^{3}-6x^{2}-72x)
integral of (1/(x^7))	\int\:(\frac{1}{x^{7}})dx
integral of cos^4(7x+7)	\int\:\cos^{4}(7x+7)dx
derivative of y=5y^2(4y^2+7)^{6/5}	derivative\:y=5y^{2}(4y^{2}+7)^{\frac{6}{5}}
(dy)/(dx)=(7x)/(3y)	\frac{dy}{dx}=\frac{7x}{3y}
tangent of 4x^2+2x	tangent\:4x^{2}+2x
tangent of y=5x-x^2	tangent\:y=5x-x^{2}
derivative of (x-1e^x)	\frac{d}{dx}((x-1)e^{x})
derivative of (ln(4x)/x)	\frac{d}{dx}(\frac{\ln(4x)}{x})
derivative of \sqrt[x]{e^1}	\frac{d}{dx}(\sqrt[x]{e^{1}})
integral of 2/(x^2)cos(2/x)	\int\:\frac{2}{x^{2}}\cos(\frac{2}{x})dx
derivative of (t^2)/2	derivative\:\frac{t^{2}}{2}
integral of 2xsqrt(x^2+5)	\int\:2x\sqrt{x^{2}+5}dx
integral of (3x)/((1-4x^2)^2)	\int\:\frac{3x}{(1-4x^{2})^{2}}dx
limit as x approaches-4 of 2x^7+8x^4-1	\lim\:_{x\to\:-4}(2x^{7}+8x^{4}-1)
integral of (ye^{y^2})	\int\:(ye^{y^{2}})dy
derivative of sqrt(x)(x-2)	derivative\:\sqrt{x}(x-2)
d/(dt)((a+bt+ct^2)/(sqrt(t)))	\frac{d}{dt}(\frac{a+bt+ct^{2}}{\sqrt{t}})
integral of tan^6(3x)	\int\:\tan^{6}(3x)dx
integral of 2sqrt(3x-1)	\int\:2\sqrt{3x-1}dx
5(d^2x)/(dt^2)+4(dx)/(dt)+9x=2cos(3t)	5\frac{d^{2}x}{dt^{2}}+4\frac{dx}{dt}+9x=2\cos(3t)

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