Utiliser la linéarité pour calculer une intégrale Exercice

I=\int_{1}^{10}\dfrac{1+8x-3x^2}{x^2} \ \mathrm dx=-\dfrac{261}{10}+8\ln\left(10\right)

I=\int_{1}^{10}\dfrac{1+8x-3x^2}{x^2} \ \mathrm dx=\dfrac{261}{10}-8\ln\left(10\right)

I=\int_{1}^{10}\dfrac{1+8x-3x^2}{x^2} \ \mathrm dx=\dfrac{281}{10}

I=\int_{1}^{10}\dfrac{1+8x-3x^2}{x^2} \ \mathrm dx=-\dfrac{9}{10}+8\ln\left(10\right)

I=\int_{1}^{2}\dfrac{x^2+x+1}{x} \ \mathrm dx=\dfrac{5}{2}+\ln\left(2\right)

I=\int_{1}^{2}\dfrac{x^2+x+1}{x} \ \mathrm dx=-\dfrac{5}{2}-\ln\left(2\right)

I=\int_{1}^{2}\dfrac{x^2+x+1}{x} \ \mathrm dx=\dfrac{1}{2}

I=\int_{1}^{2}\dfrac{x^2+x+1}{x} \ \mathrm dx=\dfrac{3}{2}+\ln\left(2\right)

I=\int_{2}^{3}\dfrac{1+xe^x}{x} \ \mathrm dx=ln\left( \dfrac{3}{2} \right)+e^3-e^2

I=\int_{2}^{3}\dfrac{1+xe^x}{x} \ \mathrm dx=-ln\left( \dfrac{3}{2} \right)-e^3+e^2

I=\int_{2}^{3}\dfrac{1+xe^x}{x} \ \mathrm dx=\dfrac{5}{36} +e^3-e^2

I=\int_{2}^{3}\dfrac{1+xe^x}{x} \ \mathrm dx=ln\left( \dfrac{2}{3} \right)+e^3-e^2

I=\int_{2}^{5}\dfrac{x+2}{x+1} \ \mathrm dx=3+\ln\left(2\right)

I=\int_{2}^{5}\dfrac{x+2}{x+1} \ \mathrm dx=-3-\ln\left(2\right)

I=\int_{2}^{5}\dfrac{x+2}{x+1} \ \mathrm dx=-\dfrac{1}{6}

I=\int_{2}^{5}\dfrac{x+2}{x+1} \ \mathrm dx=3+\ln\left(\dfrac{1}{2}\right)

I=\int_{1}^{4}\dfrac{2x}{x^2+3x} \ \mathrm dx+\int_{1}^{4}\dfrac{3}{x^2+3x} \ \mathrm dx=\ln\left(7\right)

I=\int_{1}^{4}\dfrac{2x}{x^2+3x} \ \mathrm dx+\int_{1}^{4}\dfrac{3}{x^2+3x} \ \mathrm dx=-\ln\left(7\right)

I=\int_{1}^{4}\dfrac{2x}{x^2+3x} \ \mathrm dx+\int_{1}^{4}\dfrac{3}{x^2+3x} \ \mathrm dx=\ln\left(\dfrac{1}{7}\right)

I=\int_{1}^{4}\dfrac{2x}{x^2+3x} \ \mathrm dx+\int_{1}^{4}\dfrac{3}{x^2+3x} \ \mathrm dx=\ln\left(28\right)

I=\int_{-2}^{-1}\dfrac{x}{x+7} \ \mathrm dx+\int_{-2}^{-1}\dfrac{7}{x+7} \ \mathrm dx=1

I=\int_{-2}^{-1}\dfrac{x}{x+7} \ \mathrm dx+\int_{-2}^{-1}\dfrac{7}{x+7} \ \mathrm dx=0

I=\int_{-2}^{-1}\dfrac{x}{x+7} \ \mathrm dx+\int_{-2}^{-1}\dfrac{7}{x+7} \ \mathrm dx=-1

I=\int_{-2}^{-1}\dfrac{x}{x+7} \ \mathrm dx+\int_{-2}^{-1}\dfrac{7}{x+7} \ \mathrm dx=ln6-ln5

I=\int_{0}^{3}\left(x+1\right)e^x \ \mathrm dx-\int_{0}^{3}xe^x \ \mathrm dx=e^3-1

I=\int_{0}^{3}\left(x+1\right)e^x \ \mathrm dx-\int_{0}^{3}xe^x \ \mathrm dx=1-e^3

I=\int_{0}^{3}\left(x+1\right)e^x \ \mathrm dx-\int_{0}^{3}xe^x \ \mathrm dx=e^3

I=\int_{0}^{3}\left(x+1\right)e^x \ \mathrm dx-\int_{0}^{3}xe^x \ \mathrm dx=e^3-e