$\int \frac{3^{x}}{\sqrt{16 + 9^{x}}} d x =$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$\frac{1}{\log 3} \sinh^{- 1} (\frac{3^{x}}{4}) + C$

$- \frac{1}{\log 3} \sinh^{- 1} (\frac{3^{x}}{4}) + C$

$\frac{1}{\log 3} \sin^{- 1} (\frac{3^{x}}{4}) + C$

$\frac{1}{\log 3} \cosh^{- 1} (\frac{3^{x}}{4}) + C$

answer is D.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$I = \int \frac{3^{x}}{\sqrt{16 + 9^{x}}} d x$

$\begin{array}{l} 3^{x} = t \\ \Rightarrow 3^{x} \log 3 d x = d t \end{array}$

$I = \frac{1}{\log 3} \int \frac{d t}{\sqrt{4^{2} + t^{2}}} = \frac{1}{\log 3} \sinh^{- 1} (\frac{3^{x}}{4}) + c$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test