Find $$$\int\left(\frac{8}{4 x+1}+\frac{8}{\cos ^{2}(4 x+1)}\right) \mathrm{d} x$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_22 Year：2020 Question No：6(a)

Answer:

Express $\frac{8}{\cos ^{2}(4 x+1)}$ as $8 \sec ^{2}(4 x+1)$
Integrate to obtain the form $a \ln (4 x+1)$
Integrate to obtain $b \tan (4 x+1)$
Obtain $2 \ln (4 x+1)+2 \tan (4 x+1)+c$

Knowledge points:

2.5.1 extend the idea of 'reverse differentiation' to include the integration of (Knowledge of the general method of integration by substitution is not required.)

Answer:

Knowledge points:

Solution:

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