Esercitazione IV: integrali indefiniti immediati

Integrali indefiniti immediati di vario tipo

∫ e^sin(x2+1) dx

∫ _2x/^{x2 + 1 √π} dx

Integrali indefiniti immediati di vario tipo

∫ e^sin(x2+1) dx

∫ ^2x/_{x² + 1} √π dx

209 ∫ ₁ / [(3x+1) ln(3x+1)] dx = [1/3 ln|ln(3x+1)|] + C

∫ dx/ [3x+1 ln(3x+1)] = -ln|ln(3x+1)| + C

210 ∫ [1/(1+e^x)] dx = [x-ln(1+e^x) + C]

∫ [1/(e^x+1)] dx = x - ln|e^x+1| + C

212 ∫ [2 - sin x/ (2x + cos x)] dx = [ln|2x + cos x| + C]

∫ [2 - sin x/ (e^x + cos x) dx = ln|2x + cos x| + C

∫₂₁₁ 1/(e^x + 3) dx [1/3 x - 1/3 ln(e^x + 3) + C] n^o 111 pag 578

∫ 1/(e^x + 3) dx = ∫ (1 + e^x * e^x + 3 - 3) dx / (e^x + 3)= ∫e^x + 3/(e^x + 3) dx - ∫e^x/(e^x + 3) dx -  ∫ 3 - 1/(e^x + 3) dx

3∫ 1/(e^x + 3) dx = ∫dx - ∫e^x/(e^x + 3) dx. ∫dx = x

Periodo ∫ 1/(e^x + 3) dx = 1/3∫ dx - 1/3∫ e^x/(e^x + 3) dx= 1/3 [x - ln(e^x + 3)] + C= x/3 - 1/3 ln(e^x + 3) + C= x/3 - ln(e^x + 3) + e