What is the integral of tan(x) dx?
Answer and explanation
Correct answer: C. ln|sec x| + C
- Step 1: Rewrite tan x = sin x / cos x. Let u = cos x, du = -sin x dx. Step 2. Integral is -ln|cos x| + C = ln|1/cos x| + C = ln|sec x| + C. Answer: ln|sec x| + C. Why not the others: sec^2 x is the derivative of tan x; ln|cos x| misses the required minus sign; -ln|sec x| flips the sign.
Practise more Calculus - Limits, Differential and Integral Calculus.
Free questions with an explanation for every one, and full timed Higher Secondary Certificate Examination (Bangladesh) mock tests.
More Calculus - Limits, Differential and Integral Calculus questions
- What is the limit of (sin x) / x as x approaches 0?
- What is the derivative of f(x) = x^5 - 4x^3 + 7x - 9 with respect to x?
- What is the derivative of f(x) = sin(3x) with respect to x?
- What is the derivative of f(x) = ln(x) with respect to x for x > 0?
- What is the derivative of f(x) = e^(2x) with respect to x?
- What is the slope of the tangent line to the curve y = x^2 - 3x + 2 at x = 4?