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Find the integral ∫ (tan(x))^2 dx.
Find the integral ∫ (tan(x))^2 dx.
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Practice Questions
1 question
Q1
Find the integral ∫ (tan(x))^2 dx.
tan(x) - x + C
tan(x) + x + C
tan(x) + x
tan(x) - x
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Using the identity tan^2(x) = sec^2(x) - 1, we find that ∫ (tan(x))^2 dx = tan(x) - x + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the integral ∫ (tan(x))^2 dx.
Solution:
Using the identity tan^2(x) = sec^2(x) - 1, we find that ∫ (tan(x))^2 dx = tan(x) - x + C.
Steps: 6
Show Steps
Step 1: Recall the identity for tangent squared: tan^2(x) = sec^2(x) - 1.
Step 2: Substitute this identity into the integral: ∫ (tan(x))^2 dx becomes ∫ (sec^2(x) - 1) dx.
Step 3: Split the integral into two parts: ∫ sec^2(x) dx - ∫ 1 dx.
Step 4: Calculate the first integral: ∫ sec^2(x) dx = tan(x).
Step 5: Calculate the second integral: ∫ 1 dx = x.
Step 6: Combine the results: tan(x) - x + C, where C is the constant of integration.
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