We can integrate tanx using the method integration by substitution.
In trigonometry, we know the formula for tan x, that is
Integrate both sides with respect to x.
We know that the derivative cos x is -sin x. In the integration above, sin x is multiplied by dx. Since the derivative of cos x is multiplied by dx, we can substitute a new variable y for cos x and continue the integration process.
Let y = cos x.
y = cos x
Find the derivative on both sides with respect to x.
Substitute cos x = y and sin x dx = -dy in (1).
Substitute y = cosx.
Logarithm is not defined for zero or a negative value. So, we can use absolute value for secx.
Therefore, integration of tanx is equal to ln|sec x| + c.
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