Evaluate: (5 x^3+2 x^ -5 -7 x+1 x +5 x ) d x - Vidyadip

MCQ

Evaluate: $\int\left(5 x^3+2 x^{-5}-7 x+\frac{1}{\sqrt{x}}+\frac{5}{x}\right) d x$

A
$\frac{5 x^4}{4}-\frac{1}{2 x^4}-\frac{7 x^2}{2}+2 \sqrt{x}-5 \log |x|+C$
✓
$\frac{5 x^4}{4}-\frac{1}{2 x^4}-\frac{7 x^2}{2}+2 \sqrt{x}+5 \log |x|+C$
C
$\frac{5 x^4}{4}+\frac{1}{2 x^4}+\frac{7 x^2}{2}+2 \sqrt{x}+5 \log |x|+C$
D
$\frac{5 x^4}{4}+\frac{1}{2 x^4}+\frac{7 x^2}{2}+2 \sqrt{x}-5 \log |x|+C$

✓

Answer

Correct option: B.

$\frac{5 x^4}{4}-\frac{1}{2 x^4}-\frac{7 x^2}{2}+2 \sqrt{x}+5 \log |x|+C$

We have $\int\left(5 x^3+2 x^{-5}-7 x+\frac{1}{\sqrt{x}}+\frac{5}{x}\right) d x$
$=5 \int x^3 d x+2 \int x^{-5} d x-7 \int x d x+\int x^{-1 / 2} d x+5 \int \frac{1}{x} d x$
$=5 \cdot \frac{x^4}{4}+2 \cdot \frac{x^{-4}}{(-4)}-7 \cdot \frac{x^2}{2}+\frac{x^{1 / 2}}{(1 / 2)}+5 \log |x|+C$
$=\frac{5 x^4}{4}-\frac{1}{2 x^4}-\frac{7 x^2}{2}+2 \sqrt{x}+5 \log |x|+C$

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