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Popular Calculus Problems
(dy)/(dx)=(2x(y-1))/(x^2+3)
\frac{dy}{dx}=\frac{2x(y-1)}{x^{2}+3}
integral of (1+cos(x))/(1+sin(x))
\int\:\frac{1+\cos(x)}{1+\sin(x)}dx
(\partial)/(\partial x)(5x^4+2xy+1)
\frac{\partial\:}{\partial\:x}(5x^{4}+2xy+1)
laplacetransform e^{2t}cos(3t)
laplacetransform\:e^{2t}\cos(3t)
integral of+(x^4+12x^2+1)/(x^5+20x^3+5x)
\int\:+\frac{x^{4}+12x^{2}+1}{x^{5}+20x^{3}+5x}dx
integral of 2e^x-8x
\int\:2e^{x}-8xdx
tangent of y= 5/(1+x^2),(4,0.29412)
tangent\:y=\frac{5}{1+x^{2}},(4,0.29412)
derivative of f(x)=6x^2cot(x)
derivative\:f(x)=6x^{2}\cot(x)
limit as x approaches infinity of 2x-2x
\lim\:_{x\to\:\infty\:}(2x-2x)
derivative of x^8cos(x)
\frac{d}{dx}(x^{8}\cos(x))
(\partial)/(\partial y)(y^4+5xy^3)
\frac{\partial\:}{\partial\:y}(y^{4}+5xy^{3})
integral of (54)
\int\:(54)dx
integral of (9x^2)/(sqrt(1-x^3))
\int\:\frac{9x^{2}}{\sqrt{1-x^{3}}}dx
area y=x^2-1,y=0,[0,3]
area\:y=x^{2}-1,y=0,[0,3]
derivative of f(x)= 1/4 x-1/6
derivative\:f(x)=\frac{1}{4}x-\frac{1}{6}
ty^'+9y=3t
ty^{\prime\:}+9y=3t
area 2/x ,2x,0,3
area\:\frac{2}{x},2x,0,3
(dy)/(dt)+3y=5,y(0)=1
\frac{dy}{dt}+3y=5,y(0)=1
y^{''}+16y=-24sin(4t)
y^{\prime\:\prime\:}+16y=-24\sin(4t)
integral of x^2sqrt(x^3+2)
\int\:x^{2}\sqrt{x^{3}+2}dx
sum from n=0 to infinity of 1/(4^{n+1)}
\sum\:_{n=0}^{\infty\:}\frac{1}{4^{n+1}}
derivative of e^{x^2-2x+1}
\frac{d}{dx}(e^{x^{2}-2x+1})
(\partial)/(\partial x)(x^3y^2e^{xz})
\frac{\partial\:}{\partial\:x}(x^{3}y^{2}e^{xz})
derivative of (1+e^{-2x}/(2+cos(2x)))
\frac{d}{dx}(\frac{1+e^{-2x}}{2+\cos(2x)})
integral of (cos(x/2))^2
\int\:(\cos(\frac{x}{2}))^{2}dx
tangent of f(x)=3x^3-x^2+1,(2,21)
tangent\:f(x)=3x^{3}-x^{2}+1,(2,21)
integral from-2 to 1 of 1/(x^2)
\int\:_{-2}^{1}\frac{1}{x^{2}}dx
integral of (2x)^2
\int\:(2x)^{2}dx
slope of (-2,-6),(2,2)
slope\:(-2,-6),(2,2)
tangent of f(x)=9+4x^2-2x^3,\at x=1
tangent\:f(x)=9+4x^{2}-2x^{3},\at\:x=1
derivative of y=ln(ln(x^3))
derivative\:y=\ln(\ln(x^{3}))
derivative of y=(sin(x))/(1+sin(x))
derivative\:y=\frac{\sin(x)}{1+\sin(x)}
integral of x/(x^2+3)
\int\:\frac{x}{x^{2}+3}dx
integral of (x^3)/(sqrt(x^2-49))
\int\:\frac{x^{3}}{\sqrt{x^{2}-49}}dx
derivative of 1-e^{-x^2}
\frac{d}{dx}(1-e^{-x^{2}})
limit as x approaches 2 of x^4+5^x-2
\lim\:_{x\to\:2}(x^{4}+5^{x}-2)
limit as x approaches-1 of 2x^3+3x^2-6
\lim\:_{x\to\:-1}(2x^{3}+3x^{2}-6)
integral from-1 to 3 of |x^2-2x|
\int\:_{-1}^{3}\left|x^{2}-2x\right|dx
taylor 1/(x^{1/2)}
taylor\:\frac{1}{x^{\frac{1}{2}}}
tangent of f(x)=2x^2+x-1,\at x=1
tangent\:f(x)=2x^{2}+x-1,\at\:x=1
slope of (5.6)(6.9)
slope\:(5.6)(6.9)
integral of 2r
\int\:2rdr
derivative of 7ln(x)
derivative\:7\ln(x)
y^{''}+3y^'+4y=0
y^{\prime\:\prime\:}+3y^{\prime\:}+4y=0
integral of sqrt(sin(x))cos(x)
\int\:\sqrt{\sin(x)}\cos(x)dx
integral of x/(x^3+x^2+x-3)
\int\:\frac{x}{x^{3}+x^{2}+x-3}dx
(\partial)/(\partial x)(7x+sqrt(y^4+1))
\frac{\partial\:}{\partial\:x}(7x+\sqrt{y^{4}+1})
taylor xe^{-x+1}
taylor\:xe^{-x+1}
integral of [cot(x)+1/x ]
\int\:[\cot(x)+\frac{1}{x}]dx
integral from 0 to 1 of sqrt(t^4+t^2)
\int\:_{0}^{1}\sqrt{t^{4}+t^{2}}dt
integral of (x^2+16)/x
\int\:\frac{x^{2}+16}{x}dx
integral from 0 to 2pi of 5cos(x)
\int\:_{0}^{2π}5\cos(x)dx
y^'=(y*ln(x))/(x*ln(y))
y^{\prime\:}=\frac{y\cdot\:\ln(x)}{x\cdot\:\ln(y)}
sum from n=1 to infinity of (x^n)/(9^n)
\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{9^{n}}
(dy)/(dt)+2y=3*sin(6t)
\frac{dy}{dt}+2y=3\cdot\:\sin(6t)
limit as x approaches-2-of (-1)/(x^2-4)
\lim\:_{x\to\:-2-}(\frac{-1}{x^{2}-4})
limit as x approaches 7 of 5/(x-7)
\lim\:_{x\to\:7}(\frac{5}{x-7})
derivative of (yx^2)
\frac{d}{dx}((y)x^{2})
(\partial)/(\partial x)(xzt^2sqrt(y+1))
\frac{\partial\:}{\partial\:x}(xzt^{2}\sqrt{y+1})
derivative of f(x)=e^{3e^x}
derivative\:f(x)=e^{3e^{x}}
slope of (5.4)8x^2-9y^3=-376
slope\:(5.4)8x^{2}-9y^{3}=-376
derivative of f(x)=7x^4+13x^3-22x^2+5x-3
derivative\:f(x)=7x^{4}+13x^{3}-22x^{2}+5x-3
x((dy)/(dx))=-y+2x^2y
x(\frac{dy}{dx})=-y+2x^{2}y
integral of y*e^y
\int\:y\cdot\:e^{y}dy
integral of xsin(bx)
\int\:x\sin(bx)dx
integral of-x^2+3
\int\:-x^{2}+3dx
derivative of xsqrt(x-3)
\frac{d}{dx}(x\sqrt{x-3})
integral of 3sin(2t)
\int\:3\sin(2t)dt
integral of ln(x^2+5)
\int\:\ln(x^{2}+5)dx
tangent of f(x)=4x^2-4x+1,\at x=1
tangent\:f(x)=4x^{2}-4x+1,\at\:x=1
tangent of f(x)=((x+2)/(x-2))^2,\at x=6
tangent\:f(x)=(\frac{x+2}{x-2})^{2},\at\:x=6
f^'(x)= 1/((1-x^2)^2)
f^{\prime\:}(x)=\frac{1}{(1-x^{2})^{2}}
derivative of 2x^{1/4}(x^3-11)
\frac{d}{dx}(2x^{\frac{1}{4}}(x^{3}-11))
tangent of f(x)=5x^2+4
tangent\:f(x)=5x^{2}+4
derivative of (-2/(2x+5))
\frac{d}{dx}(\frac{-2}{2x+5})
(\partial)/(\partial y)((x+y)(x^2+2y^2))
\frac{\partial\:}{\partial\:y}((x+y)(x^{2}+2y^{2}))
(dy)/(dt)+e^ty=-24e^t
\frac{dy}{dt}+e^{t}y=-24e^{t}
integral of 3^{x+2}
\int\:3^{x+2}dx
(sin(x)+cos(x))^'
(\sin(x)+\cos(x))^{\prime\:}
integral of ((x+sin(x)))/((1+cos(x)))
\int\:\frac{(x+\sin(x))}{(1+\cos(x))}dx
integral of (x+3)/(x^2(x+1)^2)
\int\:\frac{x+3}{x^{2}(x+1)^{2}}dx
(\partial)/(\partial x)(-a/x)
\frac{\partial\:}{\partial\:x}(-\frac{a}{x})
normal of y=x^2-8x,(3,-15)
normal\:y=x^{2}-8x,(3,-15)
integral of 1/(x^3+8x)
\int\:\frac{1}{x^{3}+8x}dx
f(x)=4cos(2x)
f(x)=4\cos(2x)
sum from n=0 to infinity of 4/n
\sum\:_{n=0}^{\infty\:}\frac{4}{n}
tangent of y=tan^2(x),(pi/4 ,1)
tangent\:y=\tan^{2}(x),(\frac{π}{4},1)
derivative of e^{1/2 x^2}
\frac{d}{dx}(e^{\frac{1}{2}x^{2}})
derivative of 2^{3x+1}ln(5x-11)
\frac{d}{dx}(2^{3x+1}\ln(5x-11))
laplacetransform e^{t/2}*cos(2t)
laplacetransform\:e^{\frac{t}{2}}\cdot\:\cos(2t)
integral of 9sin(ln(x))
\int\:9\sin(\ln(x))dx
integral of 2xe^{2y}
\int\:2xe^{2y}dy
integral of (x+18)sqrt(36x+x^2)
\int\:(x+18)\sqrt{36x+x^{2}}dx
derivative of f(x)=(x-2)^2
derivative\:f(x)=(x-2)^{2}
(2x+3)y^'=y+(2x+3)^{1/2}
(2x+3)y^{\prime\:}=y+(2x+3)^{\frac{1}{2}}
(\partial)/(\partial x)(e^{-2y}sin(2x))
\frac{\partial\:}{\partial\:x}(e^{-2y}\sin(2x))
integral of (9(x-9))/((x+5)(x-2))
\int\:\frac{9(x-9)}{(x+5)(x-2)}dx
derivative of ((4x^2/(2-x))^3)
\frac{d}{dx}((\frac{4x^{2}}{2-x})^{3})
integral from 0 to 2 of (2-x)^2
\int\:_{0}^{2}(2-x)^{2}dx
derivative of cos(x)
derivative\:\cos(x)
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