Integrals
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
The value of $\int \frac{e^x (1+x)}{\cos^2(e^x x)} dx$ is equal to:
(a) $\tan(e^x x) + C$
(b) $-\tan(e^x x) + C$
(c) $\cot(e^x x) + C$
(d) $-\cot(e^x x) + C$
Step-by-Step Solution
Substitute t = e^x x, dt = e^x(1+x) dx => \int sec^2 t dt = tan t + C. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\tan(e^x x) + C$: 1.0 Mark
Correct Answer: $\tan(e^x x) + C$
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