# How do you use Integration by Substitution to find #inttan(x)*sec^3(x)dx#?

Explanation

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To integrate ( \tan(x) \cdot \sec^3(x) , dx ) using integration by substitution:

- Let ( u = \sec(x) ).
- Find ( du = \sec(x) \tan(x) , dx ).
- Rewrite the integral in terms of ( u ): ( \int u^3 , du ).
- Integrate ( u^3 ) to get ( \frac{u^4}{4} ).
- Replace ( u ) with ( \sec(x) ).
- The final result is ( \frac{\sec^4(x)}{4} + C ), where ( C ) is the constant of integration.

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