integral of 5e^(-0.7x)
what is the derivative of -50/7 e^-.7x ?
∫ e^u du = e^u
u = -.7x
du = -.7 dx, so dx = du/-.7
so,
∫5e^(-.7x) dx = 5(1/-.7) e^(-.7x) + C
To find the integral of 5e^(-0.7x), we can use the power rule for integration. The power rule states that the integral of a function of the form ax^n with respect to x is (a/(n+1)) * x^(n+1) + C, where C is the constant of integration.
In this case, we have a = 5 and n = -0.7. Applying the power rule, we get:
∫ 5e^(-0.7x) dx = (5/(-0.7+1)) * e^(-0.7x + 1) + C
Simplifying further:
∫ 5e^(-0.7x) dx = (5/0.3) * e^(0.3-0.7x) + C
∫ 5e^(-0.7x) dx = (50/3) * e^(0.3-0.7x) + C
Therefore, the integral of 5e^(-0.7x) with respect to x is (50/3) * e^(0.3-0.7x) + C, where C is the constant of integration.