Integrals Test ...

Evaluate the following definite integral:

Evaluate the integral
$$\displaystyle \int_{0}^{a}\sqrt{\frac{a+x}{a-x}}dx$$

$$\displaystyle \int_{0}^{1}\sqrt{\frac{\mathrm{x}}{1-\mathrm{x}^{3}}}\mathrm{d}\mathrm{x}=$$

$$\displaystyle \int_{0}^{3}x\sqrt{1+x}dx=$$

$$\displaystyle \int_{\pi^{2}/16}^{\pi^{2}/4}\frac{\sin\sqrt{x}}{\sqrt{x}}dx=$$

$$\displaystyle \int_{0}^{1}\frac{dx}{x+\sqrt{x}}=$$

lf $$\displaystyle \int_{0}^{k}\frac{dx}{2+8x^{2}}=\frac{\pi}{16}$$ then $$\mathrm{k}=$$

Evaluate: $$\displaystyle \int_{0}^{\pi /4}\tan^{5}xdx$$

If $$\displaystyle \mathrm{U}_{\mathrm{n}}=\int^{\pi /4}_{0} \mathrm{t}\mathrm{a}\mathrm{n}^{\mathrm{n}}\theta \mathrm{d}\theta$$, then $$\mathrm{u}_{10}+\mathrm{u}_{12}$$ is equal to: