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Popular Calculus Problems
limit as x approaches 1+of arcsin(x)
\lim\:_{x\to\:1+}(\arcsin(x))
derivative of ln(ln(ln(2x)))
\frac{d}{dx}(\ln(\ln(\ln(2x))))
derivative of x^3+y
\frac{d}{dx}(x^{3}+y)
limit as x approaches infinity of x*e^x
\lim\:_{x\to\:\infty\:}(x\cdot\:e^{x})
derivative of e^{2x}(3x-2)
\frac{d}{dx}(e^{2x}(3x-2))
(4sin(t))^'
(4\sin(t))^{\prime\:}
sum from n=2 to infinity of 4/(3^n)
\sum\:_{n=2}^{\infty\:}\frac{4}{3^{n}}
expand (x^3-4x^2-6x+1)(x^2-3x+1)
expand\:(x^{3}-4x^{2}-6x+1)(x^{2}-3x+1)
derivative of-sin(2x+1)
\frac{d}{dx}(-\sin(2x)+1)
derivative of (5x-3(4x-3/x))
\frac{d}{dx}((5x-3)(4x-\frac{3}{x}))
integral of (x^3)/(x^4-8)
\int\:\frac{x^{3}}{x^{4}-8}dx
integral of (x^2)/(x^3+9)
\int\:\frac{x^{2}}{x^{3}+9}dx
derivative of (ax^2+bx+ce^{(-x)/4})
\frac{d}{dx}((ax^{2}+bx+c)e^{\frac{-x}{4}})
inverse oflaplace (s^1)/(s(s^2+s+1))
inverselaplace\:\frac{s^{1}}{s(s^{2}+s+1)}
derivative of 9x^2e^x
\frac{d}{dx}(9x^{2}e^{x})
derivative of xsinh(x-cosh(x))
\frac{d}{dx}(x\sinh(x)-\cosh(x))
integral of e^2-2cos(x)
\int\:e^{2}-2\cos(x)dx
sum from n=1 to infinity of 1/(n^{1/2)}
\sum\:_{n=1}^{\infty\:}\frac{1}{n^{\frac{1}{2}}}
derivative of y=12cos(2)(x)
derivative\:y=12\cos(2)(x)
integral of (3x)/(x^2+5)
\int\:\frac{3x}{x^{2}+5}dx
4y^'+ty=3
4y^{\prime\:}+ty=3
integral of x^5e^{2x}
\int\:x^{5}e^{2x}dx
integral of csc^2(5x)
\int\:\csc^{2}(5x)dx
integral from 1 to 7 of (t^2-4t-12)
\int\:_{1}^{7}(t^{2}-4t-12)dt
limit as x approaches 4-of 1+sqrt(4-x)
\lim\:_{x\to\:4-}(1+\sqrt{4-x})
derivative of y=(x^5+2)^2(x^4+4)^4
derivative\:y=(x^{5}+2)^{2}(x^{4}+4)^{4}
sum from n=1 to infinity of (-1)^nsin(2/n)
\sum\:_{n=1}^{\infty\:}(-1)^{n}\sin(\frac{2}{n})
derivative of sqrt(6x+4)
\frac{d}{dx}(\sqrt{6x+4})
integral from 1 to 3 of 3r^4ln(r)
\int\:_{1}^{3}3r^{4}\ln(r)dr
dy-(y-5)^2dx=0
dy-(y-5)^{2}dx=0
area x^2,2x^4,-1,1
area\:x^{2},2x^{4},-1,1
limit as x approaches 0 of 1/(sin^2(x))
\lim\:_{x\to\:0}(\frac{1}{\sin^{2}(x)})
integral from 0 to 1 of 30 1/(x^p)
\int\:_{0}^{1}30\frac{1}{x^{p}}dx
derivative of (4x+x^2)/((2+x)^2)
derivative\:\frac{4x+x^{2}}{(2+x)^{2}}
integral of u/(1+2u)
\int\:\frac{u}{1+2u}du
derivative of f(x)=2x^2-12x+8
derivative\:f(x)=2x^{2}-12x+8
integral of \sqrt[7]{e^x}
\int\:\sqrt[7]{e^{x}}dx
derivative of (x^2+y^2^3)
\frac{d}{dx}((x^{2}+y^{2})^{3})
derivative of y=(1+sin(7t))^{-6}
derivative\:y=(1+\sin(7t))^{-6}
(dy)/(dt)=(te^t)/(ysqrt(9+y^2))
\frac{dy}{dt}=\frac{te^{t}}{y\sqrt{9+y^{2}}}
derivative of y^2e^{xy-3}
\frac{d}{dx}(y^{2}e^{xy-3})
extreme f(x)=4xy
extreme\:f(x)=4xy
(1+x^2)dy=(y-cot^{-1}(x))dx
(1+x^{2})dy=(y-\cot^{-1}(x))dx
integral of 2/(1+x)
\int\:\frac{2}{1+x}dx
derivative of y=sqrt(x^3)
derivative\:y=\sqrt{x^{3}}
integral from-1 to 1 of (y^2-2)-(e^y)
\int\:_{-1}^{1}(y^{2}-2)-(e^{y})dy
derivative of x^3+2y
\frac{d}{dx}(x^{3}+2y)
limit as x approaches infinity of t^x
\lim\:_{x\to\:\infty\:}(t^{x})
limit as x approaches 4 of x^2-4x
\lim\:_{x\to\:4}(x^{2}-4x)
limit as x approaches-5 of (x+1)/(x+5)
\lim\:_{x\to\:-5}(\frac{x+1}{x+5})
f(y)=sqrt(y)
f(y)=\sqrt{y}
limit as x approaches infinity of 9/x
\lim\:_{x\to\:\infty\:}(\frac{9}{x})
y^{''}+4y=8x^2,y(0)=-3,y^'(0)=0
y^{\prime\:\prime\:}+4y=8x^{2},y(0)=-3,y^{\prime\:}(0)=0
laplacetransform 5*e^{-3x}*sin(x)*x
laplacetransform\:5\cdot\:e^{-3x}\cdot\:\sin(x)\cdot\:x
(\partial)/(\partial x)(ln(x-6y)-z)
\frac{\partial\:}{\partial\:x}(\ln(x-6y)-z)
derivative of (e^{2x}/(x^3))
\frac{d}{dx}(\frac{e^{2x}}{x^{3}})
integral of 1/(x(ln(x^2))^4)
\int\:\frac{1}{x(\ln(x^{2}))^{4}}dx
limit as x approaches 0-of (-ln(1+6x))/x
\lim\:_{x\to\:0-}(\frac{-\ln(1+6x)}{x})
integral of 2x(x^2+7)^6
\int\:2x(x^{2}+7)^{6}dx
derivative of (x^2+3/(2x))
\frac{d}{dx}(\frac{x^{2}+3}{2x})
integral of 1/(x^3+4x^2+8x)
\int\:\frac{1}{x^{3}+4x^{2}+8x}dx
integral of (7-98x)/(sqrt(4-49x^2))
\int\:\frac{7-98x}{\sqrt{4-49x^{2}}}dx
taylor e^{-9x}
taylor\:e^{-9x}
limit as x approaches 1+of 7/(x-1)
\lim\:_{x\to\:1+}(\frac{7}{x-1})
xln(x)(dy)/(dx)+y=xe^x
x\ln(x)\frac{dy}{dx}+y=xe^{x}
integral of |x-1|
\int\:\left|x-1\right|dx
integral of (-2)/(sqrt(x^2+16))
\int\:\frac{-2}{\sqrt{x^{2}+16}}dx
e^{y/x}((-ydx+xdy))/(x^2)=0
e^{\frac{y}{x}}\frac{(-ydx+xdy)}{x^{2}}=0
tangent of f(x)=(8x)/(x^2-1),(3,3)
tangent\:f(x)=\frac{8x}{x^{2}-1},(3,3)
derivative of 3x^2-5x+4
\frac{d}{dx}(3x^{2}-5x+4)
limit as x approaches 3+of sqrt(x^2-9)
\lim\:_{x\to\:3+}(\sqrt{x^{2}-9})
derivative of (x^2/(x^4+16))
\frac{d}{dx}(\frac{x^{2}}{x^{4}+16})
derivative of sqrt((x-2/(x+3)))
\frac{d}{dx}(\sqrt{\frac{x-2}{x+3}})
derivative of f(x)=e^6
derivative\:f(x)=e^{6}
(\partial)/(\partial x)(ln((xy)^z))
\frac{\partial\:}{\partial\:x}(\ln((xy)^{z}))
(\partial)/(\partial x)(x^2+w^2)
\frac{\partial\:}{\partial\:x}(x^{2}+w^{2})
limit as x approaches 0-of ln(sin(x))
\lim\:_{x\to\:0-}(\ln(\sin(x)))
sum from n=1 to infinity of 1/(n+1)
\sum\:_{n=1}^{\infty\:}\frac{1}{n+1}
integral of ((2x+2))/((x^2+1)(x-1)^3)
\int\:\frac{(2x+2)}{(x^{2}+1)(x-1)^{3}}dx
derivative of y=(arctan(2x))^2
derivative\:y=(\arctan(2x))^{2}
derivative of arctan(sqrt(x^3))
\frac{d}{dx}(\arctan(\sqrt{x^{3}}))
derivative of arcsin(5x^2)
\frac{d}{dx}(\arcsin(5x^{2}))
(\partial)/(\partial x)(x^2y-1)
\frac{\partial\:}{\partial\:x}(x^{2}y-1)
y^'=(2y+1)cot(x)
y^{\prime\:}=(2y+1)\cot(x)
derivative of (3x^2/(x^2+1))
\frac{d}{dx}(\frac{3x^{2}}{x^{2}+1})
derivative of y=(sqrt(x)-2)/(sqrt(x)+2)
derivative\:y=\frac{\sqrt{x}-2}{\sqrt{x}+2}
tangent of f(x)=7xe^x,\at x=0
tangent\:f(x)=7xe^{x},\at\:x=0
derivative of 5x^{3/5}-4
\frac{d}{dx}(5x^{\frac{3}{5}}-4)
derivative of y=(6+xf(x))/(sqrt(x))
derivative\:y=\frac{6+xf(x)}{\sqrt{x}}
integral of y^2sqrt(2y^3+1)
\int\:y^{2}\sqrt{2y^{3}+1}dy
derivative of (x^2+x+1/(x^2-x+1))
\frac{d}{dx}(\frac{x^{2}+x+1}{x^{2}-x+1})
derivative of ((x^2))/2
derivative\:\frac{(x^{2})}{2}
limit as x approaches 0 of 1/(2x^3)
\lim\:_{x\to\:0}(\frac{1}{2x^{3}})
derivative of y=(4x^2+6x)/(3x^3+2)
derivative\:y=\frac{4x^{2}+6x}{3x^{3}+2}
limit as x approaches infinity of (((e^x-e^{-x}))/((e^x+e^{-x))})+4
\lim\:_{x\to\:\infty\:}((\frac{(e^{x}-e^{-x})}{(e^{x}+e^{-x})})+4)
integral of (5cos(x)-4,x)
\int\:(5\cos(x)-4,x)dx
limit as x approaches infinity of (2-x)/(x+1)+(2^{-x}*x)/(x+2)
\lim\:_{x\to\:\infty\:}(\frac{2-x}{x+1}+\frac{2^{-x}\cdot\:x}{x+2})
y^'=2y(1-y/(6200))
y^{\prime\:}=2y(1-\frac{y}{6200})
integral from 0 to 1 of (18x)/(x^2+1)
\int\:_{0}^{1}\frac{18x}{x^{2}+1}dx
integral of (x^7e^{x^8})
\int\:(x^{7}e^{x^{8}})dx
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