What is the integral of sec(x)(sec(x)tan(x)) ?

The integral of sec(x)(sec(x)tan(x)) is (tan^2(x))/2+C

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integral of sec(x)(sec(x)tan(x))

\int sec (x) (sec (x) tan (x)) d x

\frac{tan ^{2} ( x )}{2} + C

Solution steps

\int sec (x) sec (x) tan (x) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = tan (x)

= \frac{tan ^{2} ( x )}{2}

Add a constant to the solution

= \frac{tan ^{2} ( x )}{2} + C

\int \frac{tan ( x )}{cos ( x ) sec ( sec ( x ) )} d x

\int \frac{x - 2}{3 x ^{2} - 4 x + 6} d x

\int \frac{x + cos ( x )}{x ^{2} + 2 sin ( x )} d x

\int sec^{2} (x + 2) d x

\int e^{x} (x - 1) d x

What is the integral of sec(x)(sec(x)tan(x)) ?
The integral of sec(x)(sec(x)tan(x)) is (tan^2(x))/2+C