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Popular Calculus Problems
integral of (22)/((x^2-1)^2)
\int\:\frac{22}{(x^{2}-1)^{2}}dx
limit as x approaches 0 of x(csc(x))
\lim\:_{x\to\:0}(x(\csc(x)))
y^{''}-2/7 y^'+1/49 y=0
y^{\prime\:\prime\:}-\frac{2}{7}y^{\prime\:}+\frac{1}{49}y=0
tangent of x^3-6x^2-34x+40,\at x=-2
tangent\:x^{3}-6x^{2}-34x+40,\at\:x=-2
integral of arcsec(2x)
\int\:\arcsec(2x)dx
limit as x approaches-4 of x+3
\lim\:_{x\to\:-4}(x+3)
integral of x/(x(x-2)(x+3))
\int\:\frac{x}{x(x-2)(x+3)}dx
integral of cos(3y)
\int\:\cos(3y)dy
limit as x approaches infinity of (cos(1/x))^{1/(x^2)}
\lim\:_{x\to\:\infty\:}((\cos(\frac{1}{x}))^{\frac{1}{x^{2}}})
sum from n=3 to infinity of (nx^n)/(n+2)
\sum\:_{n=3}^{\infty\:}\frac{nx^{n}}{n+2}
(dx)/(dt)-x=5t
\frac{dx}{dt}-x=5t
(\partial)/(\partial x)(1+ln(xy))
\frac{\partial\:}{\partial\:x}(1+\ln(xy))
y^{''}-8y^'+16y=t^{-2}e^{4t}
y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-2}e^{4t}
xy^2y^'=y^3-3x^3
xy^{2}y^{\prime\:}=y^{3}-3x^{3}
(\partial)/(\partial y)(x/(8+y))
\frac{\partial\:}{\partial\:y}(\frac{x}{8+y})
derivative of log_{1/x}(e)
\frac{d}{dx}(\log_{\frac{1}{x}}(e))
integral of (1+\sqrt[3]{x})/(sqrt(x))
\int\:\frac{1+\sqrt[3]{x}}{\sqrt{x}}dx
integral of csc^4(x)cot^5(x)
\int\:\csc^{4}(x)\cot^{5}(x)dx
integral of 8/(36+x^2)
\int\:\frac{8}{36+x^{2}}dx
(\partial)/(\partial x)((6x)/(3x^2+2y^2+9))
\frac{\partial\:}{\partial\:x}(\frac{6x}{3x^{2}+2y^{2}+9})
integral from 1 to infinity of 4e^{-2x}
\int\:_{1}^{\infty\:}4e^{-2x}dx
derivative of 3x^2+4x
\frac{d}{dx}(3x^{2}+4x)
derivative of (x-1*e^{x^2-4})
\frac{d}{dx}((x-1)\cdot\:e^{x^{2}-4})
integral of xln(ax)
\int\:x\ln(ax)dx
derivative of cos(xcos(y))
\frac{d}{dx}(\cos(x)\cos(y))
integral from 1 to 4 of (x^2+2)/(5x-x^2)
\int\:_{1}^{4}\frac{x^{2}+2}{5x-x^{2}}dx
tangent of sqrt(x)(25.5)
tangent\:\sqrt{x}(25.5)
derivative of x^2-4x-2
\frac{d}{dx}(x^{2}-4x-2)
tangent of f(x)=(4x)/(x+2),(2,2)
tangent\:f(x)=\frac{4x}{x+2},(2,2)
(\partial)/(\partial x)((2x+2)/(y^3))
\frac{\partial\:}{\partial\:x}(\frac{2x+2}{y^{3}})
derivative of 5x^3sqrt(25-x^2)
\frac{d}{dx}(5x^{3}\sqrt{25-x^{2}})
laplacetransform 12
laplacetransform\:12
(d^2)/(dx^2)(2x^2+5x)
\frac{d^{2}}{dx^{2}}(2x^{2}+5x)
derivative of xe^{sqrt(x)}
derivative\:xe^{\sqrt{x}}
f^{''''}=19e^{x^2}
f^{\prime\:\prime\:\prime\:\prime\:}=19e^{x^{2}}
limit as x approaches 0 of (1-x)/x
\lim\:_{x\to\:0}(\frac{1-x}{x})
derivative of 4/x+1/(5x^3+2x)
derivative\:\frac{4}{x}+\frac{1}{5x^{3}+2x}
d/(dt)(4cos(pit))
\frac{d}{dt}(4\cos(πt))
(sin(pi))^'
(\sin(π))^{\prime\:}
integral from 1 to 2 of 2(x-1)
\int\:_{1}^{2}2(x-1)dx
integral of (x^2)/(sqrt(4+x^2))
\int\:\frac{x^{2}}{\sqrt{4+x^{2}}}dx
integral of (x^4+1)/(x^3-x^2+x-1)
\int\:\frac{x^{4}+1}{x^{3}-x^{2}+x-1}dx
integral of-2e^{-x}
\int\:-2e^{-x}dx
y^{''}+y^'-2y=x^2
y^{\prime\:\prime\:}+y^{\prime\:}-2y=x^{2}
derivative of f(x)= 9/(\sqrt[5]{x)}
derivative\:f(x)=\frac{9}{\sqrt[5]{x}}
integral of (x-7)^3
\int\:(x-7)^{3}dx
y^{''}+2y^'=3+4sin(2x)
y^{\prime\:\prime\:}+2y^{\prime\:}=3+4\sin(2x)
derivative of (x^2-8x+15/(x^2+3x+2))
\frac{d}{dx}(\frac{x^{2}-8x+15}{x^{2}+3x+2})
expand (x+a)^4(x-a)^3
expand\:(x+a)^{4}(x-a)^{3}
integral of ax^2+bx+c
\int\:ax^{2}+bx+cdx
(\partial)/(\partial y)((x-y)/(xy+3))
\frac{\partial\:}{\partial\:y}(\frac{x-y}{xy+3})
limit as x approaches 0 of xln^3(1+3x^3)
\lim\:_{x\to\:0}(x\ln^{3}(1+3x^{3}))
tangent of x^4+3e^x
tangent\:x^{4}+3e^{x}
derivative of sqrt(x^2-2x)
derivative\:\sqrt{x^{2}-2x}
f(x)=-sech(x)tanh(x)
f(x)=-\sech(x)\tanh(x)
integral of 2/(sqrt(3+2x))
\int\:\frac{2}{\sqrt{3+2x}}dx
limit as x approaches 3 of x/(x-3)
\lim\:_{x\to\:3}(\frac{x}{x-3})
integral from 1 to 2 of 5x^2-4x+3
\int\:_{1}^{2}5x^{2}-4x+3dx
integral of 1/(x^2+10)
\int\:\frac{1}{x^{2}+10}dx
integral of 1/((4y)^2)
\int\:\frac{1}{(4y)^{2}}dy
inverse oflaplace (e^{1-s})/(1-s)
inverselaplace\:\frac{e^{1-s}}{1-s}
derivative of (9x^2+3)/x
derivative\:\frac{9x^{2}+3}{x}
laplacetransform sin(pit)
laplacetransform\:\sin(πt)
(\partial)/(\partial x)(xy-2x^2y)
\frac{\partial\:}{\partial\:x}(xy-2x^{2}y)
y^'+y=e^{-4t}cos(3t),y(0)=0
y^{\prime\:}+y=e^{-4t}\cos(3t),y(0)=0
x^2y^'+xy=3
x^{2}y^{\prime\:}+xy=3
integral of 1/(x(x-4))
\int\:\frac{1}{x(x-4)}dx
y^{''}-2y^'+y=((e^x))/(1+x^2)
y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{(e^{x})}{1+x^{2}}
derivative of 5e^x-b
\frac{d}{dx}(5e^{x}-b)
(x+2)^2(dy)/(dx)=5-8y-4xy
(x+2)^{2}\frac{dy}{dx}=5-8y-4xy
limit as x approaches 3-of (-5)/(x-3)
\lim\:_{x\to\:3-}(\frac{-5}{x-3})
derivative of ((-x^2+2x+2))/((x+1)^4)
derivative\:\frac{(-x^{2}+2x+2)}{(x+1)^{4}}
y^{''}+y^'-6y=2e^{5x}
y^{\prime\:\prime\:}+y^{\prime\:}-6y=2e^{5x}
(\partial)/(\partial x)(ye^{(x^2-y)})
\frac{\partial\:}{\partial\:x}(ye^{(x^{2}-y)})
2y^{''}+3y^'-2y=0
2y^{\prime\:\prime\:}+3y^{\prime\:}-2y=0
(dy)/(dx)=(4x^4y+6y^5)/(2x^5+3xy^4)
\frac{dy}{dx}=\frac{4x^{4}y+6y^{5}}{2x^{5}+3xy^{4}}
integral from 1/2 to 3 of 6xln(2x)
\int\:_{\frac{1}{2}}^{3}6x\ln(2x)dx
derivative of f(x)=2x-3
derivative\:f(x)=2x-3
(d^2)/(dx^2)(7x^{3/2})
\frac{d^{2}}{dx^{2}}(7x^{\frac{3}{2}})
inverse oflaplace 1/((s(s+1)))
inverselaplace\:\frac{1}{(s(s+1))}
f(x)= 1/(2x^2)
f(x)=\frac{1}{2x^{2}}
(\partial)/(\partial x)(1/(x^2+y^2))
\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}+y^{2}})
integral from 0 to 1 of (3x-1)^{50}
\int\:_{0}^{1}(3x-1)^{50}dx
integral of 7x^9e^{-x^5}
\int\:7x^{9}e^{-x^{5}}dx
(\partial)/(\partial x)(4e^xln(1+y))
\frac{\partial\:}{\partial\:x}(4e^{x}\ln(1+y))
limit as x approaches infinity+of (1+1/x)^{x/6}
\lim\:_{x\to\:\infty\:+}((1+\frac{1}{x})^{\frac{x}{6}})
sum from n=6 to infinity}(\sqrt{n of)/(n^2+1)
\sum\:_{n=6}^{\infty\:}\frac{\sqrt{n}}{n^{2}+1}
(\partial)/(\partial y)(x^2yz^2)
\frac{\partial\:}{\partial\:y}(x^{2}yz^{2})
(\partial)/(\partial x)(1-ln(x))
\frac{\partial\:}{\partial\:x}(1-\ln(x))
integral from 1 to 3 of x(2.25)/(x^3)
\int\:_{1}^{3}x\frac{2.25}{x^{3}}dx
y^{''}+10y^'+21y=0,y(0)=10,y^'(0)=-42
y^{\prime\:\prime\:}+10y^{\prime\:}+21y=0,y(0)=10,y^{\prime\:}(0)=-42
limit as x approaches infinity of 87
\lim\:_{x\to\:\infty\:}(87)
inverse oflaplace 8/(s^2(s-2)^3)
inverselaplace\:\frac{8}{s^{2}(s-2)^{3}}
integral of xsqrt(x-5)
\int\:x\sqrt{x-5}dx
(\partial)/(\partial x)(x^2y+ln(x))
\frac{\partial\:}{\partial\:x}(x^{2}y+\ln(x))
area 7x^2-3x,x^2-7x+2
area\:7x^{2}-3x,x^{2}-7x+2
limit as x approaches+0+of (e^x)/(e^x-1)
\lim\:_{x\to\:+0+}(\frac{e^{x}}{e^{x}-1})
integral of (28e^{4t})/(sqrt(6+e^{4t))}
\int\:\frac{28e^{4t}}{\sqrt{6+e^{4t}}}dt
(\partial)/(\partial x)(3x^7y^8+8x^5y^6)
\frac{\partial\:}{\partial\:x}(3x^{7}y^{8}+8x^{5}y^{6})
derivative of (x^{2/3}/(5+x+x^4))
\frac{d}{dx}(\frac{x^{\frac{2}{3}}}{5+x+x^{4}})
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