Evaluate $\int_0^1 \sec^3x \sin x \,dx $ Was working on some trig-based integration. I've been confident with easier ones, but can't seem to approach this one correctly.
Evaluate $\displaystyle\int_0^1 \sec^3x \sin x \,dx $
Which method of integration should I use to solve this integral?

$$
\int_0^1 sec^3(x)sin(x)dx = \int_0^1tan(x)sec^2(x)
$$
setting $u = tan(x)$
$du = sec^2(x)dx$
$dx = cos^2(x) du \therefore$
$$
\int_{tan(0)}^{tan(1)} u du
$$
$$
= \frac{tan^2(1)}{2}-\frac{tan^2(0)}{2}
$$
$$= \frac{tan^2(1)}{2}$$
