urgent

can you please help me out by telling some substitutions that can be done to solve indefinite integration

Dear student,

For terms of the form x² + a² or √x² + a², put x = a tanθ or a cotθ

          For terms of the form x² - a² or √x² – a² , put x = a sec θ or a cosecθ

          For terms of the form a² - x² or √x² + a², put x = a sin θ or a cosθ

•         If both √a+x, √a–x,  are present, then put x = a cos θ.

•         For the type √(x–a)(b–x), put x = a cos²θ + b sin²θ

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