Match the following. ∫1/x^2 - 9dx,∫secx(sec x + tan x)dx

Question

Match the following.

A	B
\(\int{\frac{1}{x^2-9}}dx\)	\(\frac{e^{3x}}{3}+c\)
\(\int secx(secx+ tanx)dx\)	secx. tanx +c secx + tanx +c
\(\int e^{3x}dx\)	\(\frac{1}{6}log|\frac{x-3}{x+3}|+c\)
\(\int (sinx + cosx)dx\)	sinx - cosx +c

Answer 1

1. 

2. ∫sec x(sec x + tan x)dx = ∫(sec² x + sec x. tan x)dx
= tanx + secx + c.

3. ∫e^3xdx = \(\frac{e^{3x}}{3}+c\).

4. ∫(sin x + cos x)dx = sin x – cosx + c.