stuart clark

Calculation of $\displaystyle \int\frac{1}{\left(1+x^4\right)^{\frac{1}{4}}}dx$ My Trial : $\displaystyle \int\frac{1}{x\cdot \left(x^{-4}+1\right)^{\frac{1}{4}}}dx$ Let $x^{-4}+1 = t^4$ and $\displaystyle \frac{1}{x^5}dx = -\frac{4t^3}{4}dt = -t^3dt$ $\displaystyle$ Now How can i solve after that Help please Thanks

find Integer solution of $3^x+4^y = y^2$

Consider the function defined by the equation $\mathbf{ y^2-2y.e^{sin^{-1}x}+x^2-1+[x]+e^{2sin^{-1}x} = 0}$, Where $\mathbf{[x] = }$ Greatest Integer function. The find area of the curve bounded by the curve and the equation $\mathbf{x = -1}$

for what value of parameter $m$ does $||x^2-4x+3|-2|=m$ have 2-solution of different sign.

for what value of $m$ does $x^2+(m+6)|x|+2m+9=0$ has 2-distinct real solution.