Integrals
NCERT Class 12
CBSE
Grade 12
Question:
$\int \dfrac{10 x^9 + 10^x \log_e 10}{x^{10} + 10^x} dx$ is equal to:
(a) $\log(x^{10} + 10^x) + C$
(b) $\log(10^x - x^{10}) + C$
(c) $(x^{10} + 10^x)^{-1} + C$
(d) $10^x + x^{10} + C$
Step-by-Step Solution
Substitute $t = x^{10} + 10^x \Rightarrow \int \frac{dt}{t} = \log(x^{10} + 10^x) + C$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating integral $= \log(x^{10} + 10^x) + C$: 1.0 Mark
Correct Answer: $\log(x^{10} + 10^x) + C$
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