What is the integral of tan(x)*sec^3(x) ?

The integral of tan(x)*sec^3(x) is 1/3 sec^3(x)+C

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integral of tan(x)*sec^3(x)

\int tan (x) \cdot sec^{3} (x) d x

\frac{1}{3} sec^{3} (x) + C

Solution steps

\int tan (x) sec^{3} (x) d x

Apply u-substitution

: \int \frac{1}{3} d u

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec^{3} (x)

= \frac{1}{3} sec^{3} (x)

Add a constant to the solution

= \frac{1}{3} sec^{3} (x) + C

\int e^{c o s (x)} sin (2 x) d x

\frac{d}{d x} (sinh^{3} (x) sin^{2} (x))

f (x) = 2 cos (x) + cos^{2} (x)

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

n \to 1 lim (3 - \frac{7}{4 ^{n}})

What is the integral of tan(x)*sec^3(x) ?
The integral of tan(x)*sec^3(x) is 1/3 sec^3(x)+C