IB Mathematics Analysis and Approaches Question Type 4: the Integrals of the Derivatives of the Inverse Trigonometric Functions in Composite Functions of Linear Changes Exercises

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

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

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

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

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

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

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

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

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