$\int (1+e^{-x})^{-1} dx =$

$\int \frac{x^3}{\sqrt{1+x^2}} dx = a(1+x^2)^{\frac{3}{2}} + b \sqrt{1+x^2} + c$,(where $c$ is the constant of integration). Find the value of $a+b$.

$\int \frac{5^{x}}{\sqrt{5^{-2x}-5^{2x}}} dx=$

$\int \frac{d x}{x^{2 / 3}\left(1+x^{2 / 3}\right)}=$

$\int \frac{30x^{14} + 15^x \log 225}{x^{15} + 15^x} dx =$

If $\int \frac{\sqrt{x}}{x(x+1)} d x = k \tan^{-1} m$,then $(k, m)$ is