1666724786535_math analyse

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Application:
Trouver les primitives suivantes :
∫ 3x 2 + 1
√x + e2x dx
= 3. 1 3 . x3 + 2√x + 1 2 . e2x + c
∫ 2x
x 2 +1 dx
= ln|x 2 + 1| + c = ln x 2 + 1 + c
∫ x2
x 3 +1 dx
= 1 3 ∫ 3x2
x 3 +1 dx
= 1 3 ln|x3 + 1| + c
∫
x
dx x 2 +1
= 1 2 ∫ 2x
x 2 +1 dx
= 1 2 ( −1
x 2 +1 ) + c
∫
x3
2√x 4 +1 dx
= 1 4 ∫
4x3
dx
2√x 4 +1
= 1 4 √x4 + 1 + c
∫
x2
√x 3 +1 dx
= 2 3 ∫
3x2
dx
2√x 3 +1
= 2 3 √x3 + 1 + c