kuvitia9f

Answered

2021-12-31

Evaluate the integrals.

$\int {x}^{3}{e}^{{x}^{4}}dx$

Answer & Explanation

ambarakaq8

Expert

2022-01-01Added 31 answers

Step 1

Solution -

Given integral -

$y=\int {x}^{3}{e}^{{x}^{4}}dx$

Let,

$t={x}^{4}$

differentiating on both sides w.r.t x,

$\frac{dt}{dx}=4{x}^{3}$

$dt=4{x}^{3}dx$

$\frac{dt}{4}={x}^{3}dx$

Step 2

Now substituting these values in the given integral,

$y=\frac{1}{4}\int {e}^{t}dt$

$y=\frac{1}{4}\left[{e}^{t}\right]+C$

where C is the constant.

Solution -

Given integral -

Let,

differentiating on both sides w.r.t x,

Step 2

Now substituting these values in the given integral,

where C is the constant.

Philip Williams

Expert

2022-01-02Added 39 answers

Step 1

This problem can be solved using a u-substitution. Let

Result:

Vasquez

Expert

2022-01-07Added 457 answers

Step 1

Substitute P

Substitute back

Result:

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