The value of (6x^{5}+3e²x}+5) \, dx is equal to

Correct Answer is : x6+32e2x+5x+kx^{6} + 3/2 e²x} + 5x + kx6+23e2x+5x+k

Correct Answer is : x6+32e2x+5x+kx^{6} + 3/2 e²x} + 5x + kx6+23e2x+5x+k

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Integral Calculus

Question : 49 of 73

Marks: +1, -0

The value of

\int (6x^{5}+3e^{2x}+5) \, dx

is equal to

Solution:

Concept:

Integrate term by term using standard formulas:

\int x^n dx = \frac{x^{n+1}}{n+1}

\int e^{ax} dx = \frac{e^{ax}}{a}

, and

\int c dx = cx

, plus the constant of integration

k

Explanation:

•

\int 6x^5 dx = 6 \cdot \frac{x^{6}}{6} = x^6

•

\int 3 e^{2x} dx = 3 \cdot \frac{e^{2x}}{2} = \frac{3}{2} e^{2x}

•

\int 5 dx = 5x

• Add the constant

k

x^{6} + \frac{3}{2} e^{2x} + 5x + k

Answer:

x^{6} + \frac{3}{2} e^{2x} + 5x + k

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