evaluatei each of the following integrals

Question

∫ (4x − 12)(x^2 − 6x + 19)^( 3/2) dx

∫ 10x^(4) e^(x^5+10) dx 

∫ (ln x)^25 /( x) dx

∫ x/(x+6) dx

∫ x/(sqrt(x+5)) dx

Answer 1

The integral is .

Power rule of integration: .

.

Answer 2

(2)

The integral is .

Integral formula: .

.

Answer 3

(3)

The integral is .

Power rule of integration: .

.

Answer 4

(4)

The integral is .

Rewrite the integral as .

Power rule of integration: .

Integral formula: .

.

Answer 5

(5)

The integral is .

Let , then .

Differentiate on each side.

.

Power rule of integration: .

Replace in the above expression.

.