Mathematics

Write the value of $$\displaystyle \int Xa^{x^{2}+1}dx$$


SOLUTION
$$P=\int Xa^{x^{2}+1}.dx$$
Let $$x^{2}+1=t$$
2x dx = dt
$$x dx = \frac{dt}{2}$$
$$P=\frac{1}{2}\int a^{t}.dt$$     we know  $$[\int a^{x}=\frac{a^{x}}{ln a}+c]$$
$$=\frac{1}{2}\frac{a^{t}}{lna}+c$$
Now $$t=x^{2}+1$$
Therefore
$$P=\frac{1}{2}\frac{a^{x^{2}+1}}{ln a}+c$$
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Subjective Medium Published on 17th 09, 2020
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