Indefinite integrals

Calcola $\int \left(5x^4-3x^2+2x-7\right)dx$.

Solution available to those who have unlocked the subject.

Calcola $\int \left(\frac{3}{x}-4\sqrt[3]{x}\right)dx$, per $x>0$.

Solution available to those who have unlocked the subject.

Calcola $\int \left(4\cos x-3\sin x+\frac{1}{1+x^2}\right)dx$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{6x+2}{3x^2+2x+5}dx$.

Solution available to those who have unlocked the subject.

Calcola $\int x^2{e}^{x^3}dx$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{\sin x}{{\cos }^{3}x}dx$, per $\cos x\ne 0$.

Solution available to those who have unlocked the subject.

Un punto materiale si muove lungo una retta con velocità $v(t)=3t^2+2t$, con $v$ in $m/s$ e $t$ in secondi. All’istante $t=1\mathrm{s}$ si trova nella posizione $s=4\mathrm{m}$. Determina la legge oraria $s(t)$ e la posizione all’istante $t=3\mathrm{s}$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{x}{\sqrt{2x+1}}dx$, per $x>-\frac{1}{2}$, con la sostituzione $t=\sqrt{2x+1}$.

Solution available to those who have unlocked the subject.

Calcola $\int x{e}^{-x}dx$.

Solution available to those who have unlocked the subject.

Calcola $\int x^2\ln xdx$, per $x>0$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{x^2+x+1}{x+2}dx$, per $x\ne -2$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{3x+4}{x^2+3x+2}dx$, per $x\ne -1$ e $x\ne -2$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{x+3}{x^2-6x+9}dx$, per $x\ne 3$.

Solution available to those who have unlocked the subject.

Calcola $\int \frac{4x-2}{x^2+2x+2}dx$.

Solution available to those who have unlocked the subject.