What is the integral of (7^x+1sin(10x)+3sec^2(x)) ?

The integral of (7^x+1sin(10x)+3sec^2(x)) is (7^x)/(ln(7))-1/10 cos(10x)+3tan(x)+C

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integral of (7^x+1sin(10x)+3sec^2(x))

\int (7^{x} + 1 sin (10 x) + 3 sec^{2} (x)) d x

\frac{7 ^{x}}{ln ( 7 )} - \frac{1}{10} cos (10 x) + 3 tan (x) + C

Solution steps

\int 7^{x} + 1 \cdot sin (10 x) + 3 sec^{2} (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 7^{x} d x + \int 1 \cdot sin (10 x) d x + \int 3 sec^{2} (x) d x

\int 7^{x} d x = \frac{7 ^{x}}{ln ( 7 )}

\int 1 \cdot sin (10 x) d x = - \frac{1}{10} cos (10 x)

\int 3 sec^{2} (x) d x = 3 tan (x)

= \frac{7 ^{x}}{ln ( 7 )} - \frac{1}{10} cos (10 x) + 3 tan (x)

Add a constant to the solution

= \frac{7 ^{x}}{ln ( 7 )} - \frac{1}{10} cos (10 x) + 3 tan (x) + C

What is the integral of (7^x+1sin(10x)+3sec^2(x)) ?
The integral of (7^x+1sin(10x)+3sec^2(x)) is (7^x)/(ln(7))-1/10 cos(10x)+3tan(x)+C