Let I(x) = ∫ dx/((x - 11)^(a/13) (x + 15)^(c/13)). If I(37) - I(24) = 1/4 (1/(5^(1/3)) - 1/(6^(1/13))), b, c N, then 3(b + c) is equal to

Integral Calculus: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q19

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

I(x) = \int \frac{dx}{(x - 11)^{\frac{a}{13}} (x + 15)^{\frac{c}{13}}}

. If

I(37) - I(24) = \frac{1}{4} \left( \frac{1}{5^{\frac{1}{3}}} - \frac{1}{6^{\frac{1}{13}}} \right)

b, c \in \mathbb{N}

, then

3(b + c)

is equal to

JEE Main 2025 Integral Calculus Question with Solution (January Unspecified (session-level dataset), Q19) | JEE Arc

JEE Main 2025 · January, Unspecified (session-level dataset) · Q19

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002

Let

I(x) = \int \frac{dx}{(x - 11)^{\frac{a}{13}} (x + 15)^{\frac{c}{13}}}

. If

I(37) - I(24) = \frac{1}{4} \left( \frac{1}{5^{\frac{1}{3}}} - \frac{1}{6^{\frac{1}{13}}} \right)

b, c \in \mathbb{N}

, then

3(b + c)

is equal to