AP EAMCET · Maths · Indefinite Integration
\(\int\left\{\frac{x}{a}+\frac{b}{x}+x^a+b^x+a b\right\} d x\) is equal to
- 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 \(\frac{x^2}{2 a}+b \log |x|+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log a}+a b x+C\)
Answer & Solution
Correct Answer
(B) \(\frac{x^2}{2 a}+b \log |x|+\frac{x^{a+1}}{a+1}+\frac{b^x}{\log b}+a b x+C\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \int\left(\frac{x}{a}+b x^{-1}+x^a+b^x+a b\right) d x \\ & =\frac{1}{a} \cdot \frac{x^2}{2}+b \log x+\frac{x^{a+1}}{a+1}+b^x \log b+a b x+C \end{aligned} \]
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