Write a value of ^ ax dx - Vidyadip

Question

Write a value of $\int\text{e}^{\text{ax}}\sin\text{bx}\text{ dx}$

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Answer

Let $\text{I}=\int\text{e}^{\text{ax}}\sin\text{bx}\text{ dx}$
We know that,
$\int\text{e}^{\text{ax}}\sin\text{bx}\text{ dx}=\frac{\text{e}^{\text{ax}}}{\text{a}^2+\text{b}^2}\big[\text{a}\sin\text{bx}-\text{b}\cos\text{bx}\big]+\text{C}$
Thus,
$\text{I}=\frac{\text{e}^{\text{ax}}}{\text{a}^2+\text{b}^2}\big[\text{a}\sin\text{bx}-\text{b}\cos\text{bx}\big]+\text{C}$

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