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Integrate the following int(dx)/(3x^2+7)

Answer»

Solution :`int(dx)/(3x^2+7)`
[PUT `x= sqrt(7/3) TAN THETA` then `dx=sqrt(7/3)sec^2theta d theta`
`(1/3)int(dx)/(x^2+(7/3))=1/3 sqrt(7/3)/(7/3)int(sec^2theta d theta)/(sec^2theta)`
(1/sqrt21)tan^(-1)((sqrt3x)/SQRT7) +C`


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