Integrations

Integration by Simple u substitution

[tlg_steps style=”steps-style-2″][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2F” title=”Calculus” icon=”ti-arrow-circle-right” subtitle=”Topics”][tlg_steps_content title=”Integration” icon=”ti-arrow-circle-right” subtitle=”Topics”][/tlg_steps] This method allows us to differentiate very complicated fractional functions or functions raised to the power of another function easily. More in this Section [tlg_blog layout=”carouseldetail” pppage=”-1″ pagination=”yes” overlay=”no-overlay” filter=”452″]

Integrating by Trigonometric Substitution

[tlg_steps style=”steps-style-2″][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2F” title=”Calculus” icon=”ti-arrow-circle-right” subtitle=”Topics”][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2Fintegration%2F|title:Introductory%20Calculus” title=”Integration” icon=”ti-arrow-circle-right” subtitle=”Topics”][/tlg_steps] This method allows us to change algebraic functions into trigonometric functions, integrate them in trigonometric forms, and return to the original algebraic functions as solutions. More in this Section [tlg_blog layout=”carouseldetail” pppage=”-1″ pagination=”yes” overlay=”no-overlay” filter=”452″]

Integrating Rational Fractions by Partial Fractions

[tlg_steps style=”steps-style-2″][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2F” title=”Calculus” icon=”ti-arrow-circle-right” subtitle=”Topics”][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2Fintegration%2F|title:Introductory%20Calculus” title=”Integration” icon=”ti-arrow-circle-right” subtitle=”Topics”][/tlg_steps] If you take a look at the integrand of the question, it seems a relatively complicated fraction. If we can split it into simpler fractions, then we may be able to integrate them easily. Making use of partial fractions to get the simpler fractions. First,…

Integration By Parts

[tlg_steps style=”steps-style-2″][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2F” title=”Calculus” icon=”ti-arrow-circle-right” subtitle=”Topics”][tlg_steps_content step_link=”url:http%3A%2F%2F127.0.0.1%2Fmkmath%2Fcalculus%2Fintegration%2F|title:Introductory%20Calculus” title=”Integration” icon=”ti-arrow-circle-right” subtitle=”Topics”][/tlg_steps] In this example, there is a product of x^2 and cosx dx in the integrand. Does simple u-substitution method work for this example? In order to use the simple u-substitution method, the relationship between two functions must be the original and its derivative each other…