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Problem If ∫ f ( x ) d x = ψ ( x ) \int f(x) dx = \psi(x) ∫ f ( x ) d x = ψ ( x ) ∫ x 5 f ( x 3 ) d x \int x^5 f(x^3) dx ∫ x 5 f ( x 3 ) d x 1 3 [ x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x ] + C \frac{1}{3} [x^3 \psi(x^3) - \int x^2 \psi(x^3) dx] + C 3 1 [ x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x ] + C 1 3 x 3 ψ ( x 3 ) − 3 ∫ x 3 ψ ( x 3 ) d x + C \frac{1}{3} x^3 \psi(x^3) - 3 \int x^3 \psi(x^3) dx + C 3 1 x 3 ψ ( x 3 ) − 3 ∫ x 3 ψ ( x 3 ) d x + C 1 3 x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x + C \frac{1}{3} x^3 \psi(x^3) - \int x^2 \psi(x^3) dx + C 3 1 x 3 ψ ( x 3 ) − ∫ x 2 ψ ( x 3 ) d x + C 1 3 [ x 3 ψ ( x 3 ) − ∫ x 3 ψ ( x 3 ) d x ] + C \frac{1}{3} [x^3 \psi(x^3) - \int x^3 \psi(x^3) dx] + C 3 1 [ x 3 ψ ( x 3 ) − ∫ x 3 ψ ( x 3 ) d x ] + C Browse the problem library