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Popular Calculus Problems
inverse oflaplace (s+4)/((s+1)^2)
inverselaplace\:\frac{s+4}{(s+1)^{2}}
integral of 1/x-2/(x^2+1)
\int\:\frac{1}{x}-\frac{2}{x^{2}+1}dx
inverse oflaplace ((-2))/((6s+s^2))
inverselaplace\:\frac{(-2)}{(6s+s^{2})}
ydx=2(x+y)dy
ydx=2(x+y)dy
(x+y)dx+(x+2y)dy=0,y(2)=3
(x+y)dx+(x+2y)dy=0,y(2)=3
limit as x approaches 0-of 1/(1+e^{1/x)}
\lim\:_{x\to\:0-}(\frac{1}{1+e^{\frac{1}{x}}})
derivative of 2arctan(4x)
\frac{d}{dx}(2\arctan(4x))
limit as x approaches 0 of x^2ln(x^2)
\lim\:_{x\to\:0}(x^{2}\ln(x^{2}))
integral of 1/((x^2-16)^{3/2)}
\int\:\frac{1}{(x^{2}-16)^{\frac{3}{2}}}dx
integral of x^{3/2}ln(x)
\int\:x^{\frac{3}{2}}\ln(x)dx
(\partial)/(\partial x)(7x^3-10x^2y+10x^2z+5xy^2-6xyz+3xz^2-y^3+y^2z)
\frac{\partial\:}{\partial\:x}(7x^{3}-10x^{2}y+10x^{2}z+5xy^{2}-6xyz+3xz^{2}-y^{3}+y^{2}z)
integral of 1/(4+4x^2)
\int\:\frac{1}{4+4x^{2}}dx
integral of 1/((x+4)^2(x-3))
\int\:\frac{1}{(x+4)^{2}(x-3)}dx
integral of 1/(x-sqrt(x))
\int\:\frac{1}{x-\sqrt{x}}dx
(dy)/(dx)=y^{2/3},y(1)=8
\frac{dy}{dx}=y^{\frac{2}{3}},y(1)=8
integral of 1/(41y^2+37y)
\int\:\frac{1}{41y^{2}+37y}dy
t^3(dy)/(dt)+3t^2y=6cos(t),y(pi)=0
t^{3}\frac{dy}{dt}+3t^{2}y=6\cos(t),y(π)=0
2(dy)/(dt)-y=4sin(3t)
2\frac{dy}{dt}-y=4\sin(3t)
tangent of f(x)=x^2+7,(1,8)
tangent\:f(x)=x^{2}+7,(1,8)
integral of 2sin(x)-3sec(x)tan(x)
\int\:2\sin(x)-3\sec(x)\tan(x)dx
integral of (t^5)/((t^2+4)^2)
\int\:\frac{t^{5}}{(t^{2}+4)^{2}}dt
derivative of ln(arccos(x))
\frac{d}{dx}(\ln(\arccos(x)))
2y^{''}+5y^'-18y=0
2y^{\prime\:\prime\:}+5y^{\prime\:}-18y=0
(dx)/(dt)=t^{3/2},x(3)=7
\frac{dx}{dt}=t^{\frac{3}{2}},x(3)=7
limit as x approaches-1 of (1+x^3)/(1+x)
\lim\:_{x\to\:-1}(\frac{1+x^{3}}{1+x})
derivative of 6x^{-1/2}
\frac{d}{dx}(6x^{-\frac{1}{2}})
tangent of y=2x^2+3/x
tangent\:y=2x^{2}+\frac{3}{x}
d/(dt)(0.1cos(10^5)t)
\frac{d}{dt}(0.1\cos(10^{5})t)
(dy)/(dx)+y/x = 1/(x^2)
\frac{dy}{dx}+\frac{y}{x}=\frac{1}{x^{2}}
integral of e^{-4x+pi}
\int\:e^{-4x+π}dx
integral of (x-5)sin(x)
\int\:(x-5)\sin(x)dx
integral of (((x+1))/(sqrt(x)))
\int\:(\frac{(x+1)}{\sqrt{x}})dx
integral of sqrt(x^8+2x^6+x^4)
\int\:\sqrt{x^{8}+2x^{6}+x^{4}}dx
3t((dy)/(dt))+y=t^2
3t(\frac{dy}{dt})+y=t^{2}
derivative of f(x)=sqrt(x^2+16)
derivative\:f(x)=\sqrt{x^{2}+16}
(2xy+2x)dx-(1+x^4)dy=0
(2xy+2x)dx-(1+x^{4})dy=0
y^'+8(tan(8x))y=10cos(8x)
y^{\prime\:}+8(\tan(8x))y=10\cos(8x)
integral of 11sin^{-3/2}(x)cos^3(x)
\int\:11\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
integral of (2^x3^x)/(9^x-4^x)
\int\:\frac{2^{x}3^{x}}{9^{x}-4^{x}}dx
limit as x approaches-1 of x^2-5x+7
\lim\:_{x\to\:-1}(x^{2}-5x+7)
xy^'-2y=-x^2-2x-1
xy^{\prime\:}-2y=-x^{2}-2x-1
y^'=xy^{-2}-2y
y^{\prime\:}=xy^{-2}-2y
x^2y^'+xy=(y^3)/x
x^{2}y^{\prime\:}+xy=\frac{y^{3}}{x}
derivative of e^{arctan(4t^2)}
derivative\:e^{\arctan(4t^{2})}
derivative of-(11/(x^5))
\frac{d}{dx}(-\frac{11}{x^{5}})
integral of xe^{6x}
\int\:xe^{6x}dx
integral of x*sin(5x)
\int\:x\cdot\:\sin(5x)dx
x(dy)/(dx)+y=x^2sin(x)
x\frac{dy}{dx}+y=x^{2}\sin(x)
integral from-pi to pi of sin^2(xco)s^3x
\int\:_{-π}^{π}\sin^{2}(xco)s^{3}xdx
((x^2+3)dy)/(dx)=xy
\frac{(x^{2}+3)dy}{dx}=xy
derivative of y=((t^2)/(t^3-4t))^3
derivative\:y=(\frac{t^{2}}{t^{3}-4t})^{3}
(dy)/(dx)=ye^x
\frac{dy}{dx}=ye^{x}
integral of-2x^2(x^3+6)^4
\int\:-2x^{2}(x^{3}+6)^{4}dx
integral of 2x^3+1/2+1/(4x^3)
\int\:2x^{3}+\frac{1}{2}+\frac{1}{4x^{3}}dx
integral from 1 to 6 of (ln(x))/(x^2)
\int\:_{1}^{6}\frac{\ln(x)}{x^{2}}dx
integral of (1/(x^2+x+1))
\int\:(\frac{1}{x^{2}+x+1})dx
implicit x^3+y^3=8xy-5
implicit\:x^{3}+y^{3}=8xy-5
(\partial)/(\partial y)((xy)/(5x+3y))
\frac{\partial\:}{\partial\:y}(\frac{xy}{5x+3y})
derivative of 2xe^xcsc(x)
derivative\:2xe^{x}\csc(x)
integral of t/(2y^4)
\int\:\frac{t}{2y^{4}}dt
integral of ((7x-4)(3x+5)^2)/(x^2)
\int\:\frac{(7x-4)(3x+5)^{2}}{x^{2}}dx
(\partial ^2)/(\partial y^2)(x/(x^2+y^2))
\frac{\partial\:^{2}}{\partial\:y^{2}}(\frac{x}{x^{2}+y^{2}})
integral of sin^5(2x)cos^2(2x)
\int\:\sin^{5}(2x)\cos^{2}(2x)dx
derivative of f(x)=sqrt(2x^2+7)
derivative\:f(x)=\sqrt{2x^{2}+7}
implicit (dy)/(dx),y=3x^5
implicit\:\frac{dy}{dx},y=3x^{5}
(\partial)/(\partial y)(x/(x^4-y^7))
\frac{\partial\:}{\partial\:y}(\frac{x}{x^{4}-y^{7}})
derivative of f(x)=(x^3)/8
derivative\:f(x)=\frac{x^{3}}{8}
integral of (ln(5x))/x
\int\:\frac{\ln(5x)}{x}dx
integral of (y^2)/(25+y^2)
\int\:\frac{y^{2}}{25+y^{2}}dy
d/(dn)((1+i)^n)
\frac{d}{dn}((1+i)^{n})
derivative of f(x)=-3/(x^4)
derivative\:f(x)=-\frac{3}{x^{4}}
integral of 0.3x^2
\int\:0.3x^{2}dx
integral of-4ln(x)
\int\:-4\ln(x)dx
(\partial)/(\partial x)(4(x-y)*e^{4y+2x^2})
\frac{\partial\:}{\partial\:x}(4(x-y)\cdot\:e^{4y+2x^{2}})
limit as x approaches 2-of tan((pix)/4)
\lim\:_{x\to\:2-}(\tan(\frac{πx}{4}))
integral of 1/(t^2sqrt(t^2-1))
\int\:\frac{1}{t^{2}\sqrt{t^{2}-1}}dt
derivative of (x^2-6x+7)/(x^2+9)
derivative\:\frac{x^{2}-6x+7}{x^{2}+9}
integral from 1 to 3 of 3/x-3/(x^2)
\int\:_{1}^{3}\frac{3}{x}-\frac{3}{x^{2}}dx
integral of x^3e^{-0.25x}
\int\:x^{3}e^{-0.25x}dx
derivative of arcsin(sqrt(2x-1))
\frac{d}{dx}(\arcsin(\sqrt{2x-1}))
derivative of 3*\sqrt[3]{x}
\frac{d}{dx}(3\cdot\:\sqrt[3]{x})
f^'(x)=3x
f^{\prime\:}(x)=3x
derivative of y=(x^3-3x)ln(2x)
derivative\:y=(x^{3}-3x)\ln(2x)
y^'+y=(e^x)/(y^2)
y^{\prime\:}+y=\frac{e^{x}}{y^{2}}
derivative of (x^2+1/(sqrt(x)))
\frac{d}{dx}(\frac{x^{2}+1}{\sqrt{x}})
derivative of sqrt(9+4x)
\frac{d}{dx}(\sqrt{9+4x})
integral of ((x^2+3))/(x^2+1)
\int\:\frac{(x^{2}+3)}{x^{2}+1}dx
limit as x approaches-2 of (3-x)^2
\lim\:_{x\to\:-2}((3-x)^{2})
integral of ((2x+1))/(x^2+1)
\int\:\frac{(2x+1)}{x^{2}+1}dx
slope of (3,8),(-7,7)
slope\:(3,8),(-7,7)
integral of sin(2x)e^{cos(2)}x
\int\:\sin(2x)e^{\cos(2)}xdx
tangent of f(x)=x^2+3x-3,\at x=2
tangent\:f(x)=x^{2}+3x-3,\at\:x=2
integral from 0 to 1 of e^{-0.1t}
\int\:_{0}^{1}e^{-0.1t}dt
derivative of y=(2cos(x))/(1+sin(x))
\frac{d}{dx}y=\frac{2\cos(x)}{1+\sin(x)}
derivative of 2cos^2(x/2)
\frac{d}{dx}(2\cos^{2}(\frac{x}{2}))
(dy)/(dx)+0.7y-18.2=0
\frac{dy}{dx}+0.7y-18.2=0
(7xy^2-3)dx+(7x^2y+4)dy=0
(7xy^{2}-3)dx+(7x^{2}y+4)dy=0
integral from 0 to 3 of sqrt(x^4+1)x^3
\int\:_{0}^{3}\sqrt{x^{4}+1}x^{3}dx
integral of (x^2+8x+1)/(x^3+12x^2+3x+6)
\int\:\frac{x^{2}+8x+1}{x^{3}+12x^{2}+3x+6}dx
integral of (-4y-1)/(y+1)
\int\:\frac{-4y-1}{y+1}dy
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