Question

Intregal sinx sec square x dx

Answer 1

Answer:

secx + c

Step-by-step explanation:

integral sinxsec^x dx

= integral sinx × 1/cos^2x

= integral( sinx/cosx × 1/cosx)

= integral (tanx secx)

= secx + c

(we know that

integral secx tanx = secx + c)

Answer 2

$\displaystyle \sf{ \int \: \sin x \: { \sec}^{2} x \: dx } = \sec x + c$

Given :

$\displaystyle \sf{ \int \: \sin x \: { \sec}^{2} x \: dx }$

To find :

The value of integral

Solution :

Step 1 of 2 :

Write down the given Integral

The given Integral is

$\displaystyle \sf{ \int \: \sin x \: { \sec}^{2} x \: dx }$

Step 2 of 2 :

Find the value of the integral

$\displaystyle \sf{ \int \: \sin x \: { \sec}^{2} x \: dx }$

$\displaystyle \sf{ = \int \: \sin x \: \: \frac{1}{ { \cos}^{2} x} \: dx }$

$\displaystyle \sf{ = \int \: \frac{ \sin x}{ { \cos}^{} x}. \frac{1}{ \cos x} \: dx }$

$\displaystyle \sf{ = \int \: \tan x \: \sec x \: dx }$

$\displaystyle \sf{ = \int \: \sec x \: \tan x \: dx }$

$\displaystyle \sf{ =\sec x + c }$

Where c is integration constant

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