Answer:
I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)
Step-by-step explanation:
for
I= ∫x^n . e^ax dx
then using integration by parts we can define u and dv such that
I= ∫(x^n) . (e^ax dx) = ∫u . dv
where
u= x^n → du = n*x^(n-1) dx
dv= e^ax dx→ v = ∫e^ax dx = (e^ax) /a ( for a≠0 .when a=0 , v=∫1 dx= x)
then we know that
I= ∫u . dv = u*v - ∫v . du + C
( since d(u*v) = u*dv + v*du → u*dv = d(u*v) - v*du → ∫u*dv = ∫(d(u*v) - v*du) =
(u*v) - ∫v*du + C )
therefore
I= ∫u . dv = u*v - ∫v . du + C = (x^n)*(e^ax) /a - ∫ (e^ax) /a * n*x^(n-1) dx +C = = (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C
I= (x^n)*(e^ax) /a - n/a ∫ (e^ax) *x^(n-1) dx +C (for a≠0)
Answer:
C
Step-by-step explanation:
Please mark brainliest
-850 feet,
-1200+800-450,
Assuming that it started at 0
Answer:
ima girafee
Step-by-step explanation:
<h2>
Answer:</h2>
The value of the given expression is -27.
<h2>Given:
</h2>
<h2>
Step-by-step explanation:
</h2>
In this problem, we need to solve the given expression in which we need to find the values of the variables. Since, the values of the variables are given, we can substitute the values and solve the equation as numerical calculation.
On substituting the values,
On squaring the values in the numerator,
On cancelling the numerator and denominator,
On adding,
