Question

integrate the following question​

Answer 1

To Integrate:

$\star \: \int \: \frac{ { \sin}^{3}x + { \cos}^{3}x }{ { \sin}^{2} x \: { \cos}^{2} x} dx$

$\implies \ \int \: \frac{ { \sin}^{3}x }{ { \sin}^{2}x \: { \cos}^{2}x } dx + \int \: \frac{ { \cos}^{3} x}{ { \sin}^{2} x \: { \cos}^{2}x } dx \\ \\ \implies \: \int \: \frac{ \sin \: x}{ { \cos}^{2}x } dx + \int \frac{ \cos \: x}{ { \sin}^{2}x } dx \\ \\ \implies \: \int \tan \: x \sec \: x \: dx + \int \: \cot \: x \cosec \: x \: dx \\ \\ \implies \: \sec \: x + \: ( - \cosec \: x) + c \\ \\ \implies \: \sec \: x - \cosec \: x + c$

•Formula :

$\star \bold{\int \: sec \: x \: tan \: x \: dx = secx \: + c } \\ \\ \star \bold{\int \: cosecx \: cotxdx = - cosecx \: + \: c}$

Answer 2

Step-by-step explanation:

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