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

The integral from-2 to 2 of 3/((x+3)^4) is 124/125

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

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

\frac{124}{125}

Decimal

0.992

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{- 2}^{2} \frac{1}{( x + 3 ) ^{4}} d x

Apply u-substitution

: \int_{1}^{5} \frac{1}{u ^{4}} d u

= 3 \cdot \int_{1}^{5} \frac{1}{u ^{4}} d u

Apply the Power Rule

: [- \frac{1}{3 u ^{3}}]_{1}^{5}

= 3 [- \frac{1}{3 u ^{3}}]_{1}^{5}

Compute the boundaries:

\frac{124}{375}

= 3 \cdot \frac{124}{375}

Simplify

= \frac{124}{125}

\int (6 x^{2} y + 2 x) d y

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\int csc (x) sec (x) d x

f (x) = 6 x

What is the integral from-2 to 2 of 3/((x+3)^4) ?
The integral from-2 to 2 of 3/((x+3)^4) is 124/125