[See Solution] Evaluate the integrals using the indicated substitutions. ∫ sec ^2(4 x+1) d x ; u=4 x+1 ∫ y √1+2 y^2 d y ; u=1+2 y^2 ∫


Question: Evaluate the integrals using the indicated substitutions.

  1. \(\int \sec ^{2}(4 x+1) d x ; u=4 x+1\)
  2. \(\int y \sqrt{1+2 y^{2}} d y ; u=1+2 y^{2}\)
  3. \(\int \sqrt{\sin \pi \theta} \cos \pi \theta d \theta ; u=\sin \pi \theta\)
  4. \(\int(2 x+7)\left(x^{2}+7 x+3\right)^{4 / 5} d x ; u=x^{2}+7 x+3\)

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