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Indefinite Integrals question

2013 · Shift 0 · Q33

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2013 · Shift 0 · Q33

Indefinite Integrals question

2013 · Shift 0 · Q33

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

If

\int {f\left( x \right)dx = \psi \left( x \right),}

then

\int {{x^5}f\left( {{x^3}} \right)dx}

is equal to

A
${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C$
B
${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C$
C
${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C$
D
${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C$

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