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tan-3-sin-d-




Question Number 129946 by bemath last updated on 21/Jan/21
 ∫ ((tan ϕ+3)/(sin ϕ)) dϕ ?
tanφ+3sinφdφ?
Answered by liberty last updated on 21/Jan/21
 T = ∫ ((1/(cos ϕ)) + (3/(sin ϕ)))dϕ   T= ∫ (sec ϕ+3csc ϕ) dϕ    T = ln ∣sec ϕ+tan ϕ∣−3ln ∣cot ϕ+csc ϕ∣ + c   T= ln ∣((1+sin ϕ)/(cos ϕ))∣−3ln ∣((cos ϕ+1)/(sin ϕ))∣+c
T=(1cosφ+3sinφ)dφT=(secφ+3cscφ)dφT=lnsecφ+tanφ3lncotφ+cscφ+cT=ln1+sinφcosφ3lncosφ+1sinφ+c

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