What is the integral of (4sqrt(x)-3x^5+(1.5)^x) ?

The integral of (4sqrt(x)-3x^5+(1.5)^x) is 2.66666…x^{3/2}-0.5x^6+2.46630…*1.5^x+C

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integral of (4sqrt(x)-3x^5+(1.5)^x)

\int (4 x - 3 x^{5} + (1.5)^{x}) d x

2.66666 \dots x^{\frac{3}{2}} - 0.5 x^{6} + 2.46630 \dots \cdot 1. 5^{x} + C

Solution steps

\int 4 x - 3 x^{5} + 1. 5^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x d x - \int 3 x^{5} d x + \int 1. 5^{x} d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 1. 5^{x} d x = 2.46630 \dots \cdot 1. 5^{x}

= \frac{8}{3} x^{\frac{3}{2}} - \frac{x ^{6}}{2} + 2.46630 \dots \cdot 1. 5^{x}

Simplify

= 2.66666 \dots x^{\frac{3}{2}} - 0.5 x^{6} + 2.46630 \dots \cdot 1. 5^{x}

Add a constant to the solution

= 2.66666 \dots x^{\frac{3}{2}} - 0.5 x^{6} + 2.46630 \dots \cdot 1. 5^{x} + C

y = x^{4} + 2 e^{x}, (0, 2)

f (x) = e^{0} (8 - 7 (0) + 5 (0)^{2})

\frac{d}{d x} (5 e)

\frac{\partial}{\partial y} ((e^{x} + e^{y})^{3})

y = 2 tan (cos (3 x)) + \frac{sin ( x ^{3} )}{x ^{2}}

What is the integral of (4sqrt(x)-3x^5+(1.5)^x) ?
The integral of (4sqrt(x)-3x^5+(1.5)^x) is 2.66666…x^{3/2}-0.5x^6+2.46630…*1.5^x+C