Find the following integrals in Exercises: (2x^2-3 +5 x ) dx - Vidyadip

Question

Find the following integrals in Exercises: $\int(2\text{x}^2-3\sin\text{x}+5\sqrt{\text{x}})\text{ dx}$

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Answer

$\int(2\text{x}^2-3\sin\text{x}+5\sqrt{\text{x}})\text{ dx}$ $=2\int\text{x}^2\text{ dx}-3\int\sin\text{x}\text{ dx}+5\int\text{x}^\frac{1}{2}\text{ dx} $ $=2\frac{\text{x}^3}{3}-3(-\cos\text{x})+5\frac{\text{x}^{\frac{1}{2}+1}}{\frac{1}{2}+1}+\text{c} $ $2\frac{\text{x}^3}{3}+3\cos\text{x}+5\frac{\text{x}^\frac{3}{2}}{\frac{3}{2}}+\text{c} $ $=2\frac{\text{x}^3}{3}+3\cos\text{x}+\frac{10}{3}\text{x}^\frac{3}{2}+\text{c} $

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