Math Problem Solver

1. \(\frac{1}{2} \int \sec^{-1} \theta \, d\theta\)

2. \(\int_1^{\sqrt{2}} \frac{dx}{\sqrt{x}(4 - x)}\)

3. \(\int_{- \ln 3}^{\ln 3} \frac{e^x}{3 + e^{2x}} \, dx\)

4. \(\int_0^3 \frac{2 \, x^3 \, dx}{5 \, (x^2 + 3)^{3/2}}\)

5. \(\int_0^1 \frac{x^2 + 10x + 3x + 36}{(x - 1)(x^2 + 4)} \, dx\)

6. \(\int_{1 - \pi}^{1 + \pi} \sec^2 \left(\frac{x - 1}{4}\right) dx\)

7. \(\int_0^2 \ln(x^2 + 2) \, dx\)

8. \(\int_{-\sqrt{2}}^{\sqrt{2}} \frac{\sqrt{2x^2 + 4}}{x^2} \, dx\)

9. \(\int_e^{e^2} \frac{\ln x}{x} \, dx\)

10. \(\int_0^1 \frac{y^4 \, dy}{4 - 2y}\)