Evaluate (1-x x) x (1-x^ 3 e^ 3 5 x ) d x .
Mathematics · JEE Main · NTA Exams — Integral Calculus
Evaluate \(\int \frac{(1-x \sin x)}{x\left(1-x^{3} e^{3 \ln 5 x}\right)} d x\).
- \(\log |t|-\frac{1}{3} \log |1-t|-\frac{1}{3} \log \left|1+t+t^{2}\right|+C_{1} \text { where } t=x e^{135 x}\)
- \(-\log |t|+\frac{1}{3} \log |1+t|+\frac{1}{3} \log \left|1+t^{2}+t\right|+C_{1} \text { where } t=x e^{[135 x}\)
- \(\log |t|+\frac{1}{3} \log |1-t|-\frac{1}{3} \log \left|1+t+t^{2}\right|+C_{1} \text { where } t=x e^{[155 x}\)
- None of these
Answer
(A) |t|- 1 3 |1-t|- 1 3 |1+t+t^ 2 |+C_ 1 where t=x e^ 135 x
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