Trigonometric Substitutions

Evaluate the following integrals using trigonometric substitution:

  1. \( \displaystyle{\int \frac{x}{\sqrt{4-x^2}} \ dx} \) Solution ↗
  2. \( \displaystyle{\int \frac{x^2}{\sqrt{9-x^2}} \ dx} \) Solution ↗
  3. \( \displaystyle{\int \frac{\sqrt{x^2-4}}{x} \ dx} \) Solution ↗
  4. \(\displaystyle{ \int_0^1 x^3 \sqrt{1-x^2} \ dx}\) Solution ↗
  5. \( \displaystyle{\int \frac{1}{\sqrt{4+x^2}} \ dx }\) Solution ↗
  6. \( \displaystyle{\int \frac{\sqrt{x^2+ 1}}{x} \ dx}\) Solution ↗
  7. \( \displaystyle{\int \frac{x^3}{\sqrt{x^2+25}} \ dx}\) Solution ↗
  8. \(\displaystyle{\int \frac{x}{\sqrt{x^2-9}} \ dx }\) Solution ↗
  9. \(\displaystyle{\int \frac{x}{\sqrt{x^2-25}} \ dx }\) Solution ↗
  10. \( \displaystyle{\int \frac{\sqrt{x^2-25}}{x^3} \ dx}\) Solution ↗
  11. \( \displaystyle{\int_0^5 \frac{dt}{\sqrt{25+t^2}}}\) Solution ↗