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Grade 12Integral Calculus

integrate the following integral
∫ 1 / 1 + sec ax dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{1}{1+secax}dx$
$I = \int \frac{cosax}{1+cosax}dx$
$I = \int \frac{1+cosax-1}{1+cosax}dx$
$I = \int dx-\int \frac{1}{1+cosax}dx$
$I = x-\int \frac{1}{2cos^{2}\frac{ax}{2}}dx$
$I = x-\int \frac{sec^{2}\frac{ax}{2}}{2}dx$
$I = x-\frac{tan\frac{ax}{2}}{2.\frac{a}{2}}+c$
$I = x-\frac{tan\frac{ax}{2}}{a}+c$

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