Evaluate. 2. EVALUATE Sx9 (3x22x+s)dx

Name: Evaluate. 2. EVALUATE Sx9 (3x22x+s)dx
Uploaded: 2024-03-20T06:46:14.000Z
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Description: Evaluate. 2. EVALUATE Sx9 (3x22x+s)dx

Given integral: ∫x4 (3x3-2x+5) dx

Answered: EVALUATE Sx9 (3x22x+s) dx

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 4E

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Expert Solution

Step 1

Given integral:

$\int x^{4} (3 x^{3} - 2 x + 5) d x$

Step 2

$\int x^{4} (3 x^{3} - 2 x + 5) d x$

Simplify the expression:

$\int (x^{4} \times 3 x^{3} - x^{4} \times 2 x + x^{4} \times 5) d x \int (3 x^{4 + 3} - 2 x^{4 + 1} + 5 x^{4}) d x \int (3 x^{7} - 2 x^{5} + 5 x^{4}) d x \int 3 x^{7} d x - \int 2 x^{5} d x + \int 5 x^{4} d x 3 \int x^{7} d x - 2 \int x^{5} d x + 5 \int x^{4} d x$

Using the power rule of integral $\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C$ , simplify:

$3 \times \frac{x^{7 + 1}}{7 + 1} - 2 \times \frac{x^{5 + 1}}{5 + 1} + 5 \times \frac{x^{4 + 1}}{4 + 1} + C \frac{3 x^{8}}{8} - \frac{2 x^{6}}{6} + \frac{5 x^{5}}{5} + C \frac{3 x^{8}}{8} - \frac{x^{6}}{3} + x^{5} + C$

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