∫tan²(x)dx
To find the integral ∫tan²(x)dx, we can use the trigonometric identity:
tan²(x) = sec²(x) – 1
Therefore, the integral can be rewritten as:
∫(sec²(x) – 1)dx
Splitting this into two separate integrals:
∫sec²(x)dx – ∫1dx
The integral of sec²(x) is a well-known trigonometric integral and its antiderivative is the tangent function:
∫sec²(x)dx = tan(x) + C1
The integral of the constant 1 with respect to x is simply x:
∫1dx = x + C2
Where C1 and C2 are constants of integration
To find the integral ∫tan²(x)dx, we can use the trigonometric identity:
tan²(x) = sec²(x) – 1
Therefore, the integral can be rewritten as:
∫(sec²(x) – 1)dx
Splitting this into two separate integrals:
∫sec²(x)dx – ∫1dx
The integral of sec²(x) is a well-known trigonometric integral and its antiderivative is the tangent function:
∫sec²(x)dx = tan(x) + C1
The integral of the constant 1 with respect to x is simply x:
∫1dx = x + C2
Where C1 and C2 are constants of integration.
Therefore, the final result of the integral ∫tan²(x)dx is:
tan(x) – x + C, where C = C1 + C2.
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