AP EAMCET · Maths · Indefinite Integration
\(\int\left(x^{3 m}+x^{2 m}+x^m\right)\left(2 x^{2 m}+3 x^m+6\right)^{\frac{1}{m}} d x=\)
- A \(\frac{1}{6(m+1)}\left(2 x^{3 m}+3 x^{2 m}+6 x^m\right)^{\frac{m+1}{m}}+C\)
- B \(\frac{1}{6(m+1)}\left(2 x^{3 m}+3 x^{2 m}+6 x^m\right)^{\frac{m-1}{m}}+C\)
- C \(\frac{1}{6(m+1)}\left(2 x^{3 m}+3 x^{2 m}+6\right)^{\frac{m+1}{m}}+C\)
- D \(\frac{1}{6(m-1)}\left(2 x^{3 m}+m x^{2 m}+6 x^m\right)^{\frac{m-1}{m}}+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{6(m+1)}\left(2 x^{3 m}+3 x^{2 m}+6 x^m\right)^{\frac{m+1}{m}}+C\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Let } \mathrm{I}=\int\left(x^{3 x}+x^{2 m}+x^m\right)\left(2 x^{2 m}+3 x m+6\right)^{\frac{1}{m}} d x \\ & =\int\left(x^{3 m}+x^{2 m}+x^m\right)\left(\left(2 x^{2 m}+3 x^m+6\right) \frac{x^m}{x^m}\right)^{\frac{1}{m}} d x \\ & =\int\left(x^{3 m-1}+x^{2…
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