Question

Match the following.
I.$\int e^x(\sin x+\cos x)dx=$ a)$e^x\tan x+c$
II.$\int e^x(\cos x-\sin x)dx=$ b)$e^x\log \sec x+c$
III.$\int e^x(\tan x+{\sec }^{2}x)dx=$ c)$e^x\sin x+c$
IV. $\int e^x(\tan x+\log \sec x)dx=$ d)$e^x\cos x+c$

• A. I-a, II- b, III- c, IV- d
• B. I-b, II- c, III- a, IV- d
• C. I-c, II- d, III- a, IV- b
• D. I-b, II- d, III- c, IV- a

Answer 1

The correct option is C I-c, II- d, III- a, IV- b

$I.\int e^x(sinx+cosx)dx=e^{x}sinx+c$

$II.\int e^x(cosx-sinx)dx=e^{x}cosx+c$

$III.\int e^x(tanx+se{c}^{2}x)dx=e^{x}tanx+c$

$IV.\int e^x\left(log\right(secx)+tanx)da=e^{x}log\left(secx\right)+c$

As they are in the form of $\int e^x\left(f\right(x)+f^1(x\left)\right)dx$ which is $=e^{x}f\left(x\right)+c$