What is the integral from-3 to 3 of ln(4x^2+4) ?

The integral from-3 to 3 of ln(4x^2+4) is 4arctan(3)+6ln(40)-12

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integral from-3 to 3 of ln(4x^2+4)

\int_{- 3}^{3} ln (4 x^{2} + 4) d x

4 arctan (3) + 6 ln (40) - 12

Decimal Notation

15.12945 \dots

Solution steps

\int_{- 3}^{3} ln (4 x^{2} + 4) d x

Apply Integration By Parts

: [x ln (4 x^{2} + 4) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{- 3}^{3}

= [x ln (4 x^{2} + 4) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{- 3}^{3}

\int \frac{2 x ^{2}}{x ^{2} + 1} d x = 2 (- arctan (x) + x)

= [x ln (4 x^{2} + 4) - 2 (- arctan (x) + x)]_{- 3}^{3}

Compute the boundaries:

4 arctan (3) + 6 ln (40) - 12

= 4 arctan (3) + 6 ln (40) - 12

\int_{0}^{11} 5 + 0.25 x^{2} d x

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\int_{0}^{t} \frac{7}{1 - x ^{2}} d x

\int_{- 1}^{2} x 2 x + 3 d x

What is the integral from-3 to 3 of ln(4x^2+4) ?
The integral from-3 to 3 of ln(4x^2+4) is 4arctan(3)+6ln(40)-12