Show work for credit when applicable. Use methods similar to those demonstrated in class. Answers without adequate justification will not receive full credit. All solutions must be in simplest form and units must be included whenever possible.
1. Evaluate ∫x³e³ˣ dx.
2. Evaluate ∫eˣ sinx dx.
3. Evaluate ∫cos³(5x)sin⁶ (5x)dx
4. Evaluate ∫sec⁴(2t) tan⁹ (2t)dt.
5. Evaluate ∫ √(1−25x²) dx