$\int 7^{7^{7^{x}}} . 7^{7^{x}} . 7^{x} d x =$

\frac{7^{7^{7^{x}}}}{(log 7)^{3}} + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{7^{7^{7^{x}}}}{(log 7)^{2}} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7^{7^{7^{x}}} . (log 7)^{3} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7^{7^{7^{x}}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{7^{7^{7^{x}}}}{(log 7)^{3}} + C$
$\int 7^{7^{7^{x}}} 7^{7^{x}} 7^{x} d x$

substitute $u = 7^{7^{x}} \to d x = \frac{7^{- 7^{x} - x}}{(log 7)^{2}} d u$

$\frac{1}{(log 7)^{2}} \int 7^{u} d u$

$\frac{1}{(log 7)^{2}} (\frac{7^{u}}{log (7)})$

$\frac{7^{u}}{(log 7)^{3}}$

$\frac{7^{7^{7^{x}}}}{(log 7)^{3}} + C$

Suggest Corrections

Similar questions

\int 7^{7^{7^{x}}} {.7}^{7^{x}} {.7}^{x} d x

\int_{a + c}^{b + c} f (x) dx

\int_{a + c}^{b + c} f (x) d x

\int_{a}^{b} f (x - c) d x

\int_{a}^{b} f (x + c) d x

\int_{a}^{b} f (x) d x

\int_{a - c}^{b - c} f (x) d x

\int e^{- 3 x} cos 7 x d x = \frac{e^{3 x}}{\sqrt{58}} [sin α cos 7 x + cos α sin 7 x] + c

sin α

cos α

The general solution of a differential equation of the type $\frac{d x}{d y} + P_{1} x = Q_{1}$ is

(a) $y e^{\int P_{1} d y} = \int (Q_{1} e^{\int P_{1} d y}) d y + C$

(b) $y e^{\int P_{1} d x} = \int (Q_{1} e^{\int P_{1} d x}) d x + C$

(d) $x e^{\int P_{1} d x} = \int (Q_{1} e^{\int P_{1} d x}) d x + C$

Join BYJU'S Learning Program