We have an answer to "∫(xa+ax+aa)dx= a.xa+1a+1+axln⁡a+c b.xa+1a+1+axln⁡a+aax+c c.xa+1a+1axln⁡a+aax+c d.xa+1a+1+axln⁡a+aax"

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pancha3

Answered question

2021-10-13

$\int (x^{a} + a^{x} + a^{a}) d x =$
a. $\frac{x^{a + 1}}{a + 1} + \frac{a^{x}}{\ln a} + c$
b. $\frac{x^{a + 1}}{a + 1} + \frac{a^{x}}{\ln a} + a^{a} x + c$
c. $\frac{x^{a + 1}}{a + 1} a^{x} \ln a + a^{a} x + c$
d. $\frac{x^{a + 1}}{a + 1} + \frac{a^{x}}{\ln a} + a^{a} x$

Answer & Explanation

Brittany Patton

Skilled2021-10-14Added 100 answers

Step 1
Consider the given integral.

\int (x^{a} + a^{x} + a^{a}) d x

Rewrite the given integral as separate integrals.

\int (x^{a} + a^{x} + a^{a}) d x = \int x^{a} d x + \int a^{x} d x + \int a^{a} d x

Step 2
Integrate using the formulas:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c

\int a^{x} d x = \frac{a^{x}}{\ln a} + c

\int a^{n} d x = a^{n} x + c

Using these formulae, the given integral can be integrated as,

\int (x^{a} + a^{x} + a^{a}) d x = \frac{x^{a + 1}}{a + 1} + \frac{a^{x}}{\ln a} + a^{a} x + C

Therefore, the correct option is B.

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