Indefinite integral

Calculus Level 1

∫ ( 2 x 2 + 4 x 3 ) d x = ? \large \int \left( \dfrac{2}{x^2}+4x^{3}\right) \, dx = \, ?

Clarification : C C denotes the arbitrary constant of integration .

− 4 x 3 + 12 x 2 + C \frac{-4}{x^3}+12x^2+C 2 x − 1 + 4 x 2 + C 2x^{-1}+4x^2+C − 2 x + x 4 + C \frac{-2}{x}+x^4+C − 4 x + 4 x 2 + C \frac{-4}{x}+4x^2+C

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Alex Harman by Alex Harman , 30, USA

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1 solution

Alex Harman
May 28, 2016

∫ 2 x 2 + 4 x 3 = ∫ 2 x − 2 + 4 x 3 = − 2 x − 1 + x 4 + C = − 2 x + x 4 + C \large \int\frac{2}{x^2}+4x^3=\int2x^{-2}+4x^3=-2x^{-1}+x^4+C=\frac{-2}{x}+x^4+C
If we take the power rule for finding derivatives, x n = n x n − 1 x^n=nx^{n-1} , and do it backwards we will get x n = 1 n + 1 x n + 1 x^n=\frac{1}{n+1}x^{n+1}

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