To integrate the given expression, we first need to simplify it by expanding e^x-1 and decomposing 1/cos^2(4x).
∫(e^x-1 - 1/cos^2(4x)) dx= ∫e^x dx - ∫1 dx - ∫sec^2(4x) dx
Next, we can integrate each term separately:∫e^x dx = e^x + C1∫1 dx = x + C2∫sec^2(4x) dx = (1/4)tan(4x) + C3
Putting it all together, we get:∫(e^x-1 - 1/cos^2(4x)) dx= e^x - x - (1/4)tan(4x) + C
Therefore, the final integrated expression is:e^x - x - (1/4)tan(4x) + C
To integrate the given expression, we first need to simplify it by expanding e^x-1 and decomposing 1/cos^2(4x).
∫(e^x-1 - 1/cos^2(4x)) dx
= ∫e^x dx - ∫1 dx - ∫sec^2(4x) dx
Next, we can integrate each term separately:
∫e^x dx = e^x + C1
∫1 dx = x + C2
∫sec^2(4x) dx = (1/4)tan(4x) + C3
Putting it all together, we get:
∫(e^x-1 - 1/cos^2(4x)) dx
= e^x - x - (1/4)tan(4x) + C
Therefore, the final integrated expression is:
e^x - x - (1/4)tan(4x) + C