If ∫ ((√x)5/(√x)7+x6) d x=α ℓ n((xβ/xβ+1))+C, then value of α and β are respectively are

Question

If ∫ ((√x)5/(√x)7+x6) d x=α ℓ n((xβ/xβ+1))+C, then value of α and β are respectively are (A) (5/2) and 2 (B) (2/5) and (5/2) (C) (5/2) and (2/5) (D) 2 and (5/2)

Tardigrade Admin · Accepted Answer

I=∫ (1/(√x)2+(√x)7) d x=∫ (1/(√x)7(1+(1)(√x)5)) d x ⇒-(5/2) (1/(√x)7) d x=d t I=-(2/5) ∫ (1/1+t) d t=-(2/5) ln (1+(1/x5 / 2))+C =(2/5) ln ((x5 / 2/x5 / 2+1))+C so α=(2/5) and β=(5/2)

Q. If $\int \frac{( x ) ^{5}}{( x ) ^{7} + x ^{6}} d x = α ℓ n (\frac{x ^{β}}{x ^{β} + 1}) + C$ , then value of $α$ and $β$ are respectively are

$\frac{5}{2}$ and 2

$\frac{2}{5}$ and $\frac{5}{2}$

$\frac{5}{2}$ and $\frac{2}{5}$

2 and $\frac{5}{2}$

Q. If ∫(x​)7+x6(x​)5​dx=αℓn(xβ+1xβ​)+C, then value of α and β are respectively are

25​ and 2

52​ and 25​

25​ and 52​

2 and 25​

I=∫(x​)2+(x​)71​dx=∫(x​)7(1+(x​)51​)1​dx ⇒−25​(x​)71​dx=dt I=−52​∫1+t1​dt=−52​ln(1+x5/21​)+C =52​ln(x5/2+1x5/2​)+C so α=52​ and β=25​

Q. If $\int \frac{( x ) ^{5}}{( x ) ^{7} + x ^{6}} d x = α ℓ n (\frac{x ^{β}}{x ^{β} + 1}) + C$ , then value of $α$ and $β$ are respectively are

$\frac{5}{2}$ and 2

$\frac{2}{5}$ and $\frac{5}{2}$

$\frac{5}{2}$ and $\frac{2}{5}$

2 and $\frac{5}{2}$