amanf

2021-10-13

Find the indefinite integral.

$\int ({x}^{2}+{2}^{-x})dx$

Ayesha Gomez

Skilled2021-10-14Added 104 answers

Step 1

Integration is summation of discrete data. The integral is calculated for the functions to find their area, displacement, volume, that occurs due to combination of small data.

Integration is of two types definite integral and indefinite integral. Indefinite integral are defined where upper and lower limits are not given, whereas in definite integral both upper and lower limit are there.

Step 2

The given integrand is$\int ({x}^{2}+{2}^{-x})dx$ , use power rule to solve the integrand

$\int ({x}^{2}+{2}^{-x})dx=\int {x}^{2}dx+\int {2}^{-x}dx$

$=\frac{{x}^{3}}{3}+\frac{{2}^{-x}}{\mathrm{ln}2}(-1)+C$ (using $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}$ )

$=\frac{{x}^{3}}{3}-\frac{{2}^{-x}}{\mathrm{ln}2}+C$

Therefore, integration of$\int ({x}^{2}+{2}^{-x})dx\text{}is\text{}\frac{{x}^{3}}{3}-\frac{{2}^{-x}}{\mathrm{ln}2}+C$

Integration is summation of discrete data. The integral is calculated for the functions to find their area, displacement, volume, that occurs due to combination of small data.

Integration is of two types definite integral and indefinite integral. Indefinite integral are defined where upper and lower limits are not given, whereas in definite integral both upper and lower limit are there.

Step 2

The given integrand is

Therefore, integration of

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