1) evaluate: integral of
(3x^2 + 5x - 1 + 3/x) dx
x^3/3 + x^2/5 - x Is this correct?
2) evaluate: integral of
(5e^7x + srqtx) dx
I am not sure with this. Could you please explain. Thank you for you help!
what about the INT 3/x dx term?
That is 3lnx
Int 5e^7x = 5/7 e^7x
INT sqrtx= 2/3 x^3/2
o ok thank you.
1) To solve the integral ∫(3x^2 + 5x - 1 + 3/x) dx, we can break it down into individual integrals and use the power rule of integration.
∫(3x^2) dx = x^3
∫(5x) dx = 5/2 * x^2
∫(-1) dx = -x
∫(3/x) dx = 3 * ln|x|
Combining these individual integrals, we get:
∫(3x^2 + 5x - 1 + 3/x) dx = x^3 + 5/2 * x^2 - x + 3 * ln|x| + C
So, x^3/3 + x^2/2 - x + 3ln|x| + C is not the correct answer. The correct answer is x^3 + 5/2 * x^2 - x + 3 * ln|x| + C, where C is the constant of integration.
2) To evaluate the integral ∫(5e^(7x) + √x) dx, we again break it down into individual integrals.
∫(5e^(7x)) dx = (5/7) * e^(7x) (using the chain rule)
∫(√x) dx = (2/3) * x^(3/2) (using the power rule of integration)
So, the integral can be simplified to:
∫(5e^(7x) + √x) dx = (5/7) * e^(7x) + (2/3) * x^(3/2) + C
Where C is the constant of integration. Therefore, (5/7) * e^(7x) + (2/3) * x^(3/2) + C is the correct answer.