Question

Giúp mình vs toán 1 đh ạ cảm ơn nhiều

Answer 1

1: \(\int\left(t^5-e^{2t}\right)dt=\frac16\cdot t^6-\frac12\cdot e^{2t}+C\)

2: \(\int\left(\sin x-\sqrt{x}\right)\mathrm{d}x=\int\sin x\mathrm{d}x-\int\left(\sqrt{x}\right)\mathrm{d}x\)

\(=-cosx-\int\left(x^{\frac12}\right)\mathrm{d}x+C\)

\(=-cosx-\frac{1}{\frac12+1}\cdot x^{\frac12+1}+C=-cosx-\frac23\cdot x^{\frac32}+C\)

3: \(\int\left(\frac{x^2+\sqrt{x}+3}{x^2}\right)\mathrm{d}x=\int\left(1+x^{-\frac32}+\frac{3}{x^2}\right)\mathrm{d}x\)

\(=x+x^{-\frac32+1}\cdot\frac{1}{-\frac32+1}+C=x-2\cdot x^{-\frac12}+C\)