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Hasil ∫ 3 x 2 ( 2 x 3 + 5 ) d x = ...

Hasil $\int 3 x^{2} (2 x^{3} + 5) d x$ = ...

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begin mathsize 12px style u equals 2 x cubed plus 5 d u equals 6 x squared plus d x 1 half d u equals 3 x squared d x end style

$begin mathsize 12px style integral 3 x squared square root of open parentheses 2 x cubed plus 5 close parentheses end root d x equals integral 1 half square root of u d u equals 1 half integral u to the power of 1 half end exponent d u equals 1 half open square brackets fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction times u to the power of 1 half plus 1 end exponent close square brackets plus C equals 1 half open square brackets 2 over 3 times u to the power of 3 over 2 end exponent close square brackets plus C equals 1 third u to the power of 3 over 2 end exponent plus C equals 1 third open parentheses 2 x cubed plus 5 close parentheses to the power of 3 over 2 end exponent plus C equals 1 third open parentheses 2 x cubed plus 5 close parentheses to the power of 1 open parentheses 2 x cubed plus 5 close parentheses to the power of 1 half end exponent plus C equals 1 third open parentheses 2 x cubed plus 5 close parentheses square root of open parentheses 2 x cubed plus 5 close parentheses end root plus C end style$