`int (4t^2 + 3)^2 dx` Find the indefinite integral.

Textbook Question

Chapter 4, 4.1 - Problem 24 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`int(4t^2+3)^2dt`

`=int(16t^4+24t^2+9)dt`

apply the sum rule and power rule,

`=int16t^4dt+int24t^2dt+int9dt`

`=16(t^(4+1)/(4+1))+24(t^(2+1)/(2+1))+9t`

`=(16t^5)/5+8t^3+9t+C`

C is constant

scisser's profile pic

scisser | (Level 3) Honors

Posted on

Foil out the function:

`(4x^2+3)^2=16x^4+24x^2+9`

`int(16x^4+24x^2+9)dx`

Use the antiderivative rule: `int (a^n=(a^(n+1))/(n+1))`

`=(16x^5)/5+8x^3+9x + C`

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