What is the integral of sec^x(x ?

The integral of sec^x(x is (xsec^x(d))/(ln(sec(d)))-1/(ln^2(sec(d)))sec^x(d)+C

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integral of sec^x(x

\int sec^{x} (d) x d x

\frac{x sec ^{x} ( d )}{ln ( sec ( d ) )} - \frac{1}{ln ^{2} ( sec ( d ) )} sec^{x} (d) + C

Solution steps

\int sec^{x} (d) x d x

Apply Integration By Parts

: \frac{x sec ^{x} ( d )}{ln ( sec ( d ) )} - \int \frac{sec ^{x} ( d )}{ln ( sec ( d ) )} d x

= \frac{x sec ^{x} ( d )}{ln ( sec ( d ) )} - \int \frac{sec ^{x} ( d )}{ln ( sec ( d ) )} d x

\int \frac{sec ^{x} ( d )}{ln ( sec ( d ) )} d x = \frac{1}{ln ^{2} ( sec ( d ) )} sec^{x} (d)

= \frac{x sec ^{x} ( d )}{ln ( sec ( d ) )} - \frac{1}{ln ^{2} ( sec ( d ) )} sec^{x} (d)

Add a constant to the solution

= \frac{x sec ^{x} ( d )}{ln ( sec ( d ) )} - \frac{1}{ln ^{2} ( sec ( d ) )} sec^{x} (d) + C

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What is the integral of sec^x(x ?
The integral of sec^x(x is (xsec^x(d))/(ln(sec(d)))-1/(ln^2(sec(d)))sec^x(d)+C