Find the indefinite integral. ∫(x2+2−x)dx

Question

Find the indefinite integral.   ∫(x2+2−x)dx

Ayesha Gomez · Accepted Answer

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}) d x

, use power rule to solve the integrand

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

= \frac{x^{3}}{3} + \frac{2^{- x}}{\ln 2} (- 1) + C

(using

\int x^{n} d x = \frac{x^{n + 1}}{n + 1}

)

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

Therefore, integration of

\int (x^{2} + 2^{- x}) d x i s \frac{x^{3}}{3} - \frac{2^{- x}}{\ln 2} + C

Find the indefinite integral. \int (x^{2}+2^{-x})dx

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