tanx dx
The expression “tanx dx” is an integral expression, specifically the integral of the tangent function with respect to x
The expression “tanx dx” is an integral expression, specifically the integral of the tangent function with respect to x.
To solve this integral, we can use a technique called integration by substitution. Let’s consider the substitution u = tan(x), then we can differentiate both sides to find du = sec^2(x) dx. This allows us to rewrite the integral in terms of u:
∫ tan(x) dx = ∫ (u) (sec^2(x) dx)
Substituting in the expression for du, we have:
= ∫ u du
Now we can easily integrate u with respect to u:
= (1/2) u^2 + C
Substituting back for u, we have:
= (1/2) tan^2(x) + C
So, the integral of tan(x) dx is equal to (1/2) tan^2(x) + C, where C is the constant of integration.
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