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Chapter 5: Q 39. (page 429)

Solve the integral: $鈭� \ln (x^{3}) d x$ .

Short Answer

Expert verified

The required answer is $3 x (\ln (x) - 1) + c$ .

Step by step solution

Step 1. Given information.

We have given integral is $鈭� \ln (x^{3}) d x$ .

Step 2. Solve the integration by parts .

We have,

$u = \ln x d u = \frac{d x}{x}$

and

$d v = d x v = 鈭� d x v = x$

The formula of integration by parts is $鈭� u d v = u v - 鈭� v d u$ .

$鈭� \ln (x^{3}) d x = 3 (\ln (x) x - 鈭� x \frac{1}{x} d x) = 3 (x \ln (x) - 鈭� 1 d x) = 3 x \ln (x) - 3 x + c = 3 x (\ln (x) - 1) + c$

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Solve the integral:鈭�lnx3dx.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the integration by parts .

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Solve the integral: $鈭� \ln (x^{3}) d x$ .