12 grade maths others
∫ sec4x dx
∫ sec4x dx
1 Answer
Askiitians Tutor Team
Approved Tutor Answer9 Months agoTo solve the integral of sec(4x) with respect to x, we can use a standard technique involving a substitution. Here’s a step-by-step breakdown:
Step 1: Substitution
Let’s set:
- u = 4x
This means:
- du = 4 dx
- dx = du/4
Step 2: Rewrite the Integral
Now, we can rewrite the integral:
∫ sec(4x) dx = ∫ sec(u) (du/4)
This simplifies to:
(1/4) ∫ sec(u) du
Step 3: Integral of Secant
The integral of sec(u) is a known result:
∫ sec(u) du = ln |sec(u) + tan(u)| + C
Step 4: Substitute Back
Now, substituting back for u:
(1/4) [ln |sec(4x) + tan(4x)|] + C
Final Answer
The final result for the integral ∫ sec(4x) dx is:
(1/4) ln |sec(4x) + tan(4x)| + C
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