What is the integral from 1 to x^4 of sec(t) ?

The integral from 1 to x^4 of sec(t) is ln|tan(x^4)+sec(x^4)|-ln(tan(1)+sec(1))

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integral from 1 to x^4 of sec(t)

\int_{1}^{x^{4}} sec (t) d t

ln tan (x^{4}) + sec (x^{4}) - ln (tan (1) + sec (1))

Solution steps

\int_{1}^{x^{4}} sec (t) d t

Use the common integral:

\int sec (t) d t = ln ∣ tan (t) + sec (t) ∣

= [ln ∣ tan (t) + sec (t) ∣]_{1}^{x^{4}}

Compute the boundaries:

ln tan (x^{4}) + sec (x^{4}) - ln (tan (1) + sec (1))

= ln tan (x^{4}) + sec (x^{4}) - ln (tan (1) + sec (1))

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What is the integral from 1 to x^4 of sec(t) ?
The integral from 1 to x^4 of sec(t) is ln|tan(x^4)+sec(x^4)|-ln(tan(1)+sec(1))