IB Mathematics Analysis and Approaches Question Type 2: Trigonometric Substitution in Integrals Exercises

Find $$\int \frac{x^2}{\sqrt{4-x^2}}\mathrm{d}x$$

Find $$\int \frac{x^3}{\sqrt{4-x^2}}dx$$

Find $$\int \sqrt{x^2+9}dx$$

Evaluate $$\int \sqrt{4-x^2}dx$$

Find $$\int \sqrt{x^2-9}dx$$

Evaluate $$\int \frac{x^2}{\sqrt{x^2-9}}dx$$

Compute $$\int \frac{x^3}{(x^2+4{)}^{\frac{3}{2}}}dx$$

Evaluate $$\int \frac{x}{\sqrt{4-x^2}}dx$$

Find $$\int \frac{dx}{x\sqrt{x^2+4}}$$