   Chapter 4.5, Problem 24E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ d t cos 2 t 1 + tan t

To determine

To evaluate:

The indefiniteintegral dtcos2t1+tant

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

xn dx=xn+1n+1+C  n-1

2) Given:

dtcos2t1+tant

3) Calculation:

Here, use the substitution method because the differential of the function 1+tant is sec2tdt=dtcos2t present in the integral.

Substitute u=1+tant.

Differentiate u=1+tant with respectto t

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