Integration of tanx

Tanx represents the tangent function of x, where x is the variable. Integration of tanx involves finding the antiderivative of tanx. The antiderivative is a function whose derivative is equal to the original function.

Basic integral of tanx

The integral of tanx can be represented as ∫tanx dx.

Using trigonometric identities

To integrate tanx, we can use trigonometric identities to rewrite the expression in a more manageable form. One useful identity is:

tan^2x = sec^2x - 1

Using this identity, we can rewrite the integral of tanx as:

∫tanx dx = ∫(sec^2x - 1) dx

Integration of sec^2x

The integral of sec^2x is well-known and can be easily evaluated. The integral of sec^2x dx is equal to tanx + C, where C is the constant of integration.

Therefore, the integral of tanx can be rewritten as:

∫tanx dx = ∫(sec^2x - 1) dx = ∫sec^2x dx - ∫1 dx = tanx - x + C

Conclusion

In conclusion, the integration of tanx can be determined by using trigonometric identities to rewrite the expression in a more manageable form. By applying the identity that relates tanx to sec^2x, we can simplify the integral and evaluate it. The final result is tanx - x + C, where C represents the constant of integration.