Integral ∫(5x3+7x2−2x+5) ( 5 x 3 + 7 x 2 − 2 x + 5 ) dx

Assessment: JAMB UTME - Mathematics - 2015 Subject: General Mathematics

Question 1 Report

Integral ∫ $(5 x^{3} + 7 x^{2} - 2 x + 5)$ dx

\frac{5 x^{4}}{4} + \frac{7 x^{3}}{3} + 2 x + C

\frac{5 x}{4} + \frac{7 x^{3}}{3} - x^{2} + 5 x + C

\frac{5 x^{3}}{3} + \frac{7 x^{2}}{x} - x + C

\frac{2 x^{2}}{3} + \frac{x}{5} - C

Answer Details

$\int [(x^{2} + 4 x^{2} + 1) \div x^{2}] d x = \int (x^{3} / x^{2}) d x + \int (1 / x^{2}) d x$
⇒ $\int x d x + \int 4^{- 1} o r + \int (1 / x^{2}) d x$
= $x^{2} / 2 - 4 x - 1 / x^{2} + C$

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