exo7 825

$\displaystyle \int_0^1 \frac{dx}{x^2+2}$.

$\displaystyle \int_{-1/2}^{1/2} \frac{dx}{1-x^2}$.

$\displaystyle \int_2^3 \frac{2x+1}{x^2+x-3}\,dx$.

$\displaystyle \int_0^2 \frac{x\,dx}{x^4+16}$.

$\displaystyle \int_0^3 \frac{x^4+6x^3-5x^2+3x-7}{(x-4)^3}\,dx$.

$\displaystyle \int_{-2}^0 \frac{dx}{x^3-7x+6}$.

$\displaystyle \int_{-1}^1 \frac{2x^4+3x^3+5x^2+17x+30}{x^3+8}\,dx$.

$\displaystyle \int_2^3 \frac{4x^2}{x^4-1}\,dx$.

$\displaystyle \int_{-1}^0 \frac{x^3+2x+1}{x^3-3x+2}\,dx$.

$\displaystyle \int_1^2 \frac{2x^8+5x^6-12x^5+30x^4+36x^2+24} {x^4(x^2+2)^3}\,dx$.

$\displaystyle \int_0^a \frac{-2x^2+6x+7} {x^4+5x^2+4}\,dx$ pour $a\in \mathbb{R}$. Y a-t-il une limite quand $a\to+\infty$ ?

$\displaystyle \int_0^2 \frac{dx}{x^4+1}$.