Question

Write the value of $\int X{a}^{x^2+1}dx$

Answer 1

$P=\int X{a}^{x^2+1}.dx$

Let $x^2+1=t$

2x dx = dt

$xdx=\frac{dt}{2}$

$P=\frac{1}{2}\int a^t.dt$ we know $[\int a^x=\frac{a^x}{lna}+c]$

$=\frac{1}{2}\frac{a^t}{lna}+c$

Now $t=x^2+1$

Therefore

$P=\frac{1}{2}\frac{a^{x^2+1}}{lna}+c$