If f(x) d x= (x) , then x^ 5 f (x^ 3 ) d x is equal to
Mathematics · JEE Main · NTA Exams — Integral Calculus
If \(\int f(x) d x=\Psi(x)\), then \(\int x^{5} f\left(x^{3}\right) d x\) is equal to
- \(\frac{1}{3}\left[x^{3} \psi\left(x^{3}\right)-\int x^{2} \psi\left(x^{3}\right) d x\right]+C\)
- \(\frac{1}{3} x^{3} \psi\left(x^{3}\right)-3 \int x^{3} \psi\left(x^{3}\right) d x+C\)
- \(\frac{1}{3} x^{3} \psi\left(x^{3}\right)-\int x^{2} \psi\left(x^{3}\right) d x+C\)
- \(\frac{1}{3}\left[x^{3} \psi\left(x^{3}\right)-\int x^{3} \psi\left(x^{3}\right) d x\right]+C\)
Answer
(A) 1 3 [x^ 3 (x^ 3 )- x^ 2 (x^ 3 ) d x ]+C
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