U substitution help?

integrate [3(cosx)^2 (sinx)]dx on the interval from 0 to pi

and if you were told to integrate (tanx)^2 over the interval from 0 to pi/4 what would it be? do you have to use substitution for this one?


also for this one i don't know why they took out the 5?

u substitution for 5x/(4+x^2)^2

1 Answer

  • Best Answer

    Alright... U generally look for the deepest buried function to call variable "u", on the condition that its derivative of some sort is outside. Since (cosx) is inside the bracket, lets make u=cosx...Notice sin x is outside the bracket..


    du/dx= -sinx Differentiate implicitly

    du= -sinx dx Cross multiply

    -du= sinx dx

    Now substitute..

    S 3(u)^2 du S is integral

    u^3 now u substitue u for cosx...so (cosx)^3, which u can then plug in the values


    is the same as (sinx/cosx) again can be done through substitution as above..except that ur dividing instead of multiplying..

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