Question

Selesaikan integral tak tentu fungsi trigonometri

Answer 1

∫x.e^(-x²) dx

= ∫x.e^(-x²) d(-x²)/(-2x)
= ∫e^(-x²) d(-x²) / (-2)
= -1/2 ∫e^(-x²) d(-x)²
= -1/2 e^(-x²) + C

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∫(x³/(⁴√(x⁴+3)) dx
= ∫x³/((x⁴+3)^(1/4)) d(x⁴+3)/(4x³)
= ∫1/(x⁴+3)^(1/4) d(x⁴+3) / 4
= 1/4 ∫1/(x⁴+3)^(1/4) d(x⁴+3)
= 1/4 ∫(x⁴+3)^(-1/4) d(x⁴+3)
= 1/4 (3/4)(x⁴+3)^(3/4) + C
= 3/16 (x⁴+3)^(3/4) + C
= 3/16 ⁴√(x⁴+3)³ + C