Question

Use the formula $$ \int \sin^{-1}(u) du = u \sin^{-1}(u) + \sqrt{1 - u^2} + C $$ to evaluate the following integral. $$ \int x \arcsin(3x^2) dx $$

Name: use the formula int sin 1u du u sin 1u sqrt1 u2 c to evaluate the following integral int x arcsin3x2 dx 17115
Uploaded: 2022-04-06T12:09:43-08:00
Duration: 6 min 34 s
Channel: Sirat Shah
Description: use the formula int sin 1u du u sin 1u sqrt1 u2 c to evaluate the following integral int x arcsin3x2 dx 17115

          Use the formula
$$ \int \sin^{-1}(u) du = u \sin^{-1}(u) + \sqrt{1 - u^2} + C $$
to evaluate the following integral.
$$ \int x \arcsin(3x^2) dx $$

Added by Christopher W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sirat Shah

04/06/2022

Step 1

Step 2: Identify the substitution needed. The given integral is $\int x \arcsin(3x^2) dx$. The formula involves $\sin^{-1}(u)$ (which is the same as $\arcsin(u)$). Let $u = 3x^2$. Then, we need to find $du$. $du = \frac{d}{dx}(3x^2) dx = 6x dx$. Step 3: Adjust Show more…

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