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stuart clark

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  1. Calculation of [math]\displaystyle \int\frac{1}{\left(1+x^4\right)^{\frac{1}{4}}}dx[/math] My Trial : [math]\displaystyle \int\frac{1}{x\cdot \left(x^{-4}+1\right)^{\frac{1}{4}}}dx[/math] Let [math]x^{-4}+1 = t^4[/math] and [math]\displaystyle \frac{1}{x^5}dx = -\frac{4t^3}{4}dt = -t^3dt[/math] [math]\displaystyle [/math] Now How can i solve after that Help please Thanks
  2. find Integer solution of [math]3^x+4^y = y^2[/math]
  3. Consider the function defined by the equation [math]\mathbf{ y^2-2y.e^{sin^{-1}x}+x^2-1+[x]+e^{2sin^{-1}x} = 0}[/math], Where [math] \mathbf{[x] = }[/math] Greatest Integer function. The find area of the curve bounded by the curve and the equation [math]\mathbf{x = -1}[/math]
  4. for what value of parameter [math] m [/math] does [math] ||x^2-4x+3|-2|=m [/math] have 2-solution of different sign.
  5. for what value of [math] m [/math] does [math]x^2+(m+6)|x|+2m+9=0[/math] has 2-distinct real solution.
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