Integral calculus

Compute

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

Solution available to those who have unlocked the subject.

Compute

$$\int \frac{{\left(\ln x\right)}^2}{x}dx.$$

Solution available to those who have unlocked the subject.

Compute

$$\int x\cos xdx.$$

Solution available to those who have unlocked the subject.

Compute

$$\int \arctan xdx.$$

Solution available to those who have unlocked the subject.

Compute

$$\int \frac{1}{\sqrt{x}(1+x)}dx.$$

Solution available to those who have unlocked the subject.

Compute

$$\int \frac{e^{2x}}{e^x+1}dx.$$

Solution available to those who have unlocked the subject.

Compute

$$\int \frac{1}{x^2-9}dx.$$

Solution available to those who have unlocked the subject.

Compute

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

Solution available to those who have unlocked the subject.

Compute

$$\int \frac{1}{x^2+4x+8}dx.$$

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Compute

$${\int }_1^e\frac{\sqrt{\ln x}}{x}dx.$$

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Compute the area of the region between the parabola $y=4-x^2$ and the $x$-axis.

Solution available to those who have unlocked the subject.

Compute

$$\underset{x\to 0}{\lim }\frac{{\int }_0^x\ln (1+t)dt}{x^2}.$$

Solution available to those who have unlocked the subject.

Given

$$F(x)={\int }_x^{x^2}{e}^{-t^2}dt,$$

compute $F^{\prime }(x)$ and the value $F^{\prime }(1)$.

Solution available to those who have unlocked the subject.

Compute

$${\int }_{-2}^2|x+1|dx.$$

Solution available to those who have unlocked the subject.