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:<math> = \int_0^\frac{\pi}{4}\sin{x}\,(\frac{\sin{x}}{\cos^3{x}})\,dx</math>
:<math> = \int_0^\frac{\pi}{4}\sin{x}\,(\frac{\sin{x}}{\cos^3{x}})\,dx</math>
:<math> = \frac{\sin{x}}{2\cos^2{x}})\int_0^\frac{\pi}{4}\frac{1}{2\cos{x}},\,dx</math>
:<math> = \frac{\sin{x}}{2\cos^2{x}} - \int_0^\frac{\pi}{4}\frac{sec{x}}{2},\,dx</math>
Recall that:
:\int{sec{x},\,dx = tan{x}</math>
and the solution becomes obvious.
[[category:mathematics]]
[[category:mathematics]]
[[category:calculus]]
[[category:calculus]]