-x-x2-x3-x4 d x is equal toA- 1-x-x2-x3-CB- x 2- x 3- x 4- x 5- CC- x2-2-x3-3-x4-4-x5-5-CD- 1-2 x-3 x2-4 x3-C

The correct option is C x^22+ x^33+ x^44+ x^55 +C∫ (x+ x^2 +x^3 +x^4) dx = ∫ x dx + ∫ x^2 dx + ∫ x^3 dx + ∫ x^4 dx = x^1+11+1 +x^2+12+1+x^3+13+1+ x^4+14+1 ...

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Byju's Answer

Standard XII

Mathematics

How to Find the Inverse of a Function

∫x+x2+x3+x4 d...

Question

$\int (x + x^{2} + x^{3} + x^{4})$ dx is equal to

1 + x + x^{2} + x^{3} + C

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1 + 2 x + 3 x^{2} + 4 x^{3} + C

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x^{2} + x^{3} + x^{4} + x^{5} + C

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

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Solution

The correct option is D $\frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \frac{x^{5}}{5} + C$
$\int (x + x^{2} + x^{3} + x^{4}) d x$
$= \int x d x + \int x^{2} d x + \int x^{3} d x + \int x^{4} d x$
$= \frac{x^{1 + 1}}{1 + 1} + \frac{x^{2 + 1}}{2 + 1} + \frac{x^{3 + 1}}{3 + 1} + \frac{x^{4 + 1}}{4 + 1}$
= $\frac{x^{2}}{2} + \frac{x^{3}}{3} + \frac{x^{4}}{4} + \frac{x^{5}}{5} + C$

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∫(x+x2+x3+x4) dx is equal to

The correct option is D x22+x33+x44+x55+C∫(x+x2+x3+x4)dx =∫x dx+∫x2dx+∫x3 dx+∫x4dx =x1+11+1+x2+12+1+x3+13+1+x4+14+1 = x22+x33+x44+x55+C

$\int (x + x^{2} + x^{3} + x^{4})$ dx is equal to