Find out the answer to "Evaluate the following integrals. ∫x210x3dx"

Chaya Galloway

Answered question

2021-02-24

Evaluate the following integrals.

\int x^{2} 10^{x^{3}} d x

Answer & Explanation

Asma Vang

Skilled2021-02-25Added 93 answers

$The given integral is,$
$\int x^{2} 10^{x^{3}} d x$
$Using substitution method of integration, on substituting x^{3} with t$
$x^{3} = t$
$3 x^{2} d x = d t$
$x^{2} d x = \frac{d t}{3}$
$Then the transformed integral we get is,$
$I = \int \frac{10^{t}}{3} d t$
$= \frac{1}{3} \int 10^{t} d t$
$Using exponential rule, \int a^{x} d x = \frac{a^{x}}{\ln (a)} + C$
$I = \frac{1}{3} \int 10^{t} d t$
$= \frac{1}{3} [\frac{10^{t}}{\ln (10)}] + C$
$On puttinf back the value of t, we get$
$I = \frac{10^{x^{3}}}{3 \ln (10)} + C$
$Therefore, the value of the given integral is \frac{10^{x^{3}}}{3 \ln (10)} + C$

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