Question

$\int e^x(\tanh x+\sec h^{2}x)dx=$

• A. $e^x\tan hx+c$
• B. $e^{x}sec{h}^{2}x+c$ $
• C. $e^{x}sinhx+c$
• D. $e^x$cosec$h^{2}x+c$

Answer 1

The correct option is A $e^x\tan hx+c$

$\int e^x(\tanh x+sec{h}^{2}x)dx$

$\frac{d\tan hx}{dx}=\sec h^{2}x$

$\int e^x(\tan hx+d\frac{\tan hx}{dx})dx$

It is in the form $\int e^x\left(f\right(x)+f^{{}^{\prime }}(x\left)\right)dx$

$=e^{x}f\left(x\right)+c$

$=e^x\tanh x+c$

$\int e^x(\tanh x+sec{h}^{2}x)dx=e^x\tanh x+c$