∫ 2m x ⋅ 3n x d x when m, n ∈ N is equal to:

Question

∫ 2m x ⋅ 3n x d x when m, n ∈ N is equal to: (A) (2m x+3n x/m ℓ n 2+n ℓ n 3)+c (B) ((m n) ⋅ 2x ⋅ 3x/m ℓ n 2+n ℓ n 3)+c  (C)  (2m x ⋅ 3n x/ ln (2m ⋅ 3n))+c (D) none of these

Tardigrade Admin · Accepted Answer

I=∫ 2m x ⋅ 3n x d x=∫(2m ⋅ 3n)x d x=(2m x ⋅ 3n x/ ln (2m ⋅ 3n))+c

Q. $\int 2^{m x} \cdot 3^{n x} d x$ when $m, n \in N$ is equal to:

$\frac{2 ^{m x} + 3 ^{n x}}{m ℓ n 2 + n ℓ n 3} + c$

$\frac{( mn ) \cdot 2 ^{x} \cdot 3 ^{x}}{m ℓ n 2 + n ℓ n 3} + c$

$\frac{2 ^{m x} \cdot 3 ^{n x}}{l n ( 2 ^{m} \cdot 3 ^{n} )} + c$

none of these

$I = \int 2^{m x} \cdot 3^{n x} d x = \int (2^{m} \cdot 3^{n})^{x} d x = \frac{2 ^{m x} \cdot 3 ^{n x}}{l n ( 2 ^{m} \cdot 3 ^{n} )} + c$

Q. ∫2mx⋅3nxdx when m,n∈N is equal to:

mℓn2+nℓn32mx+3nx​+c

mℓn2+nℓn3(mn)⋅2x⋅3x​+c

ln(2m⋅3n)2mx⋅3nx​+c