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Integral - direct method

1. Review the basic formulas of integration by the direct method

Solution:

Indefinite integral:

indefinite-integral-direct-method-1a 

f(x) dx is the integrand, F(x) is the antiderivative, C is the integration constant

 indefinite-integral-direct-method-1


2. Calculate the integrals:

indefinite-integral-direct-method-2z 

Solution:

indefinite-integral-direct-method-2r 


3. Calculate the integrals:

indefinite-integral-direct-method-3z

Solution:

indefinite-integral-direct-method-3r


4. Calculate the integrals:

indefinite-integral-direct-method-4z

Solution:

indefinite-integral-direct-method-4r


5. Calculate the integrals:

indefinite-integral-direct-method-5z

Solution:

indefinite-integral-direct-method-5r


6. Calculate the integrals:

indefinite-integral-direct-method-6z

Solution:

indefinite-integral-direct-method-6r


7. Calculate the integrals:

indefinite-integral-direct-method-7z

Solution:

indefinite-integral-direct-method-7r


8. Calculate the integrals:

indefinite-integral-direct-method-8z

Solution:

indefinite-integral-direct-method-8r

 

9. Calculate the integrals:

indefinite-integral-direct-method-9z

Solution:

indefinite-integral-direct-method-9r