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Question: Answered & Verified by Expert
$\int\left\{\frac{x}{a}+\frac{b}{x}+x^a+b^x+a b\right\} d x$ is equal to
MathematicsIndefinite IntegrationAP EAMCETAP EAMCET 2021 (23 Aug Shift 1)
Options:
  • A $\frac{x^2}{2 a}+\frac{b}{x^2}+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log b}+C$
  • B $\frac{x^2}{2 a}+b \log |x|+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log b}+a b x+C$
  • C $\frac{1}{a}+b \log |x|+a x^{a-1}+b^x \log b+a b+C$
  • D $\frac{x^2}{2 a}+b \log |x|+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log a}+a b x+C$
Solution:
1380 Upvotes Verified Answer
The correct answer is: $\frac{x^2}{2 a}+b \log |x|+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log b}+a b x+C$
$$
\begin{aligned}
& \int\left(\frac{x}{a}+b x^{-1}+x^a+b^x+a b\right) d x \\
& =\frac{1}{a} \cdot \frac{x^2}{2}+b \log x+\frac{x^{a+1}}{a+1}+b^x \log b+a b x+C
\end{aligned}
$$

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