int x^{2019} cdot e^{x^{2020}} , dx = . . . | vedclass

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Question

(A) To solve the integral $\int x^{2019} \cdot e^{x^{2020}} \, dx$,we use the method of substitution.Let $u = x^{2020}$.Then,differentiating both side

Vedclass · Accepted Answer

$\frac{1}{2020} e^{x^{2020}}$

Vedclass · Answer

(A) To solve the integral $\int x^{2019} \cdot e^{x^{2020}} \, dx$,we use the method of substitution.Let $u = x^{2020}$.Then,differentiating both sides with respect to $x$,we get $\frac{du}{dx} = 2020 x^{2019}$.This implies $du = 2020 x^{2019} \, dx$,or $x^{2019} \, dx = \frac{1}{2020} \, du$.Substituting these into the original integral:$\int e^u \cdot \frac{1}{2020} \, du = \frac{1}{2020} \int e^u \, du$.The integral of $e^u$ is $e^u$,so we have $\frac{1}{2020} e^u + C$.Finally,substituting $u = x^{2020}$ back,we get $\frac{1}{2020} e^{x^{2020}} + C$.Therefore,the correct option is $A$.

$\int x^{2019} \cdot e^{x^{2020}} \, dx = $ . . . . . . $+ C$.

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