Question Type 4: The integrals of the derivatives of the inverse trigonometric functions in composite functions of linear changes Exercises

Evaluate the integral $\displaystyle \int \frac{3\,dx}{\sqrt{4 - 9(x - 1)^2}}$.

Evaluate the integral $\displaystyle \int \frac{dx}{1 + (3x + 2)^2}$.

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{3 - x^2 - 2x}}$.

Evaluate the integral $\displaystyle \int \frac{5\,dx}{4 + (2x - 3)^2}$.

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{2x - x^2}}$.

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{1 - (2x)^2}}$.

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{6x - x^2}}$.

Evaluate the integral $\displaystyle \int \frac{dx}{\sqrt{4 - (x - 1)^2}}$.

Evaluate the integral $\displaystyle \int \frac{dx}{(5x + 2)^2 + 9}$.