JEE Main 2013Session, Shift 1MathematicsMediumIntegral Calculus369× since 2002If ∫f(x)dx=ψ(x),\int {f\left( x \right)dx = \psi \left( x \right),}∫f(x)dx=ψ(x), then ∫x5f(x3)dx\int {{x^5}f\left( {{x^3}} \right)dx}∫x5f(x3)dx is equal toAOption A. 13[x3ψ(x3)−∫x2ψ(x3)dx]+C{1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C31[x3ψ(x3)−∫x2ψ(x3)dx]+CBOption B. 13x3ψ(x3)−3∫x3ψ(x3)dx+C{1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C31x3ψ(x3)−3∫x3ψ(x3)dx+CCOption C. 13x3ψ(x3)−∫x2ψ(x3)dx+C{1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C31x3ψ(x3)−∫x2ψ(x3)dx+CDOption D. 13[x3ψ(x3)−∫x3ψ(x3)dx]+C{1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C31[x3ψ(x3)−∫x3ψ(x3)dx]+CCheckSkip · show solution
