Step by step solution to "Evaluate the integral, if it exists. ∫(8x3+3x2)dx"

hionormf

Answered question

2021-12-09

Evaluate the integral, if it exists.

\int (8 x^{3} + 3 x^{2}) d x

censoratojk

Beginner2021-12-10Added 46 answers

Step 1
Given-

\int (8 x^{3} + 3 x^{2}) d x

To evaluate- The above integral.
Formula used- The power rule,

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

, where C is the constant.
Step 2
Explanation- Rewrite the given integral as

I = \int (8 x^{3} + 3 x^{2}) d x

Now, using the power rule as

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

, we get,

I = (\frac{8 x^{4}}{4} + \frac{3 x^{3}}{3}) + C

= (2 x^{4} + x^{3}) + C

So, the value of the inteegral is

(2 x^{4} + x^{3}) + C

.
Answer- Hence, the value of the integral

I = \int (8 x^{3} + 3 x^{2}) d x i s (2 x^{4} + x^{3}) + C

, where C is arbitrary constant.

Toni Scott

Beginner2021-12-11Added 32 answers

\int (8 x^{3} + 3 x^{2}) d x

Lets

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