Immediate indefinite integrals (2)

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Compute the following indefinite integrals:

• (a) $\displaystyle\int x^{4}\,dx$
• (b) $\displaystyle\int (3x^{2}-2x+1)\,dx$
• (c) $\displaystyle\int \sqrt{x}\,dx$
• (d) $\displaystyle\int \frac{1}{x^{2}}\,dx$

Solution

• (a) $\dfrac{x^{5}}{5}+C$.
• (b) $x^{3}-x^{2}+x+C$.
• (c) $\dfrac23 x^{3/2}+C$.
• (d) $-\dfrac1x+C$.